Not true! Don't the Pharisees have any say in the matter? Paul said to the Jews belonged the "oracles of God" (Romans 3:2). Jesus often referred to Moses and the Prophets as speaking of Him. He used these Scriptures, referring to them as "it is written" dozens of times in His refutation against the religious leaders and even Satan (during the temptation). In fact:
Jesus gave what many theologians consider to be a validation of the books that make up what we know as the Old Testament when he said, Therefore, behold, I am sending you prophets and wise men and scribes; some of them you will kill and crucify, and some of them you will scourge in your synagogues, and persecute from city to city, so that upon you may fall the guilt of all the righteous blood shed on earth, from the blood of righteous Abel to the blood of Zechariah, the son of Berechiah, whom you murdered between the temple and the altar. (Matthew 23:34,35) This a speaking of the first and last chronological books that make up the sacred Scriptures. Also, from http://www.the-highway.com/ntcanon_Warfield.html, we learn:
But the Old Testament books were not the only ones which the apostles (by Christ’s own appointment the authoritative founders of the church) imposed upon the infant churches, as their authoritative rule of faith and practice. No more authority dwelt in the prophets of the old covenant than in themselves, the apostles, who had been “made sufficient as ministers of a new covenant “; for (as one of themselves argued) “if that which passeth away was with glory, much more that which remaineth is in glory.” Accordingly not only was the gospel they delivered, in their own estimation, itself a divine revelation, but it was also preached “in the Holy Ghost” (I Pet. i. 12); not merely the matter of it, but the very words in which it was clothed were “of the Holy Spirit” (I Cor. ii. 13). Their own commands were, therefore, of divine authority (I Thess. iv. 2), and their writings were the depository of these commands (II Thess. ii. 15). “If any man obeyeth not our word by this epistle,” says Paul to one church (II Thess. iii. 14), “note that man, that ye have no company with him.” To another he makes it the test of a Spirit-led man to recognize that what he was writing to them was “the commandments of the Lord” (I Cor. xiv. 37). Inevitably, such writings, making so awful a claim on their acceptance, were received by the infant churches as of a quality equal to that of the old “Bible “; placed alongside of its older books as an additional part of the one law of God; and read as such in their meetings for worship — a practice which moreover was required by the apostles (I Thess. v. 27; Col. iv. 16; Rev. 1. 3). In the apprehension, therefore, of the earliest churches, the “Scriptures” were not a closed but an increasing “canon.” Such they had been from the beginning, as they gradually grew in number from Moses to Malachi; and such they were to continue as long as there should remain among the churches “men of God who spake as they were moved by the Holy Ghost.”
We say that this immediate placing of the new books — given the church under the seal of apostolic authority — among the Scriptures already established as such, was inevitable. It is also historically evinced from the very beginning. Thus the apostle Peter, writing in A.D. 68, speaks of Paul’s numerous letters not in contrast with the Scriptures, but as among the Scriptures and in contrast with “the other Scriptures” (II Pet. iii. 16) — that is, of course, those of the Old Testament. In like manner the apostle Paul combines, as if it were the most natural thing in the world, the book of Deuteronomy and the Gospel of Luke under the common head of “Scripture” (I Tim. v. 18): “For the Scripture saith, ‘Thou shalt not muzzle the ox when he treadeth out the corn’ [Deut. xxv. 4]; and, ‘The laborer is worthy of his hire’” (Luke x. 7). The line of such quotations is never broken in Christian literature. Polycarp (c. 12) in A.D. 115 unites the Psalms and Ephesians in exactly similar manner: “In the sacred books, . . . as it is said in these Scriptures, ‘Be ye angry and sin not,’ and ‘Let not the sun go down upon your wrath.’” So, a few years later, the so-called second letter of Clement, after quoting Isaiah, adds (ii. 4): “And another Scripture, however, says, ‘I came not to call the righteous, but sinners’” — quoting from Matthew, a book which Barnabas (circa 97-106 A.D.) had already adduced as Scripture. After this such quotations are common.
What needs emphasis at present about these facts is that they obviously are not evidences of a gradually-heightening estimate of the New Testament books, originally received on a lower level and just beginning to be tentatively accounted Scripture; they are conclusive evidences rather of the estimation of the New Testament books from the very beginning as Scripture, and of their attachment as Scripture to the other Scriptures already in hand. The early Christians did not, then, first form a rival “canon” of “new books” which came only gradually to be accounted as of equal divinity and authority with the “old books”; they received new book after new book from the apostolical circle, as equally” Scripture “ with the old books, and added them one by one to the collection of old books as additional Scriptures, until at length the new books thus added were numerous enough to be looked upon as another section of the Scriptures.
The earliest name given to this new section of Scripture was framed on the model of the name by which what we know as the Old Testament was then known. Just as it was called “The Law and the Prophets and the Psalms” (or “the Hagiographa”), or more briefly “The Law and the Prophets,” or even more briefly still “The Law”; so the enlarged Bible was called “The Law and the Prophets, with the Gospels and the Apostles” (so Clement of Alexandria, “Strom.” vi. 11, 88; Tertullian, “De Præs. Hær.” 36), or most briefly “The Law and the Gospel” (so Claudius Apolinaris, Irenæus); while the new books apart were called “The Gospel and the Apostles,” or most briefly of all” The Gospel.” This earliest name for the new Bible, with all that it involves as to its relation to the old and briefer Bible, is traceable as far back as Ignatius (A.D. 115), who makes use of it repeatedly (e.g., “ad Philad.” 5; “ad Smyrn.” 7). In one passage he gives us a hint of the controversies which the enlarged Bible of the Christians aroused among the Judaizers (“ad Philad.” 6). “When I heard some saying,” he writes, “‘Unless I find it in the Old [Books] I will not believe the Gospel,’ on my saying, ‘It is written,’ they answered, ‘That is the question.’ To me, however, Jesus Christ is the Old [Books]; his cross and death and resurrection, and the faith which is by him, the undefiled Old [Books] — by which I wish, by your prayers, to be justified. The priests indeed are good, but the High Priest better,” etc. Here Ignatius appeals to the “Gospel” as Scripture, and the Judaizers object, receiving from him the answer in effect which Augustine afterward formulated in the well-known saying that the New Testament lies hidden in the Old and the Old Testament is first made clear in the New. What we need now to observe, however, is that to Ignatius the New Testament was not a different book from the Old Testament, but part of the one body of Scripture with it; an accretion, so to speak, which had grown upon it.
I hope you will take a look at the two links I gave because they do explain quite well how the Bible (Old and New Testaments) we now know came to be and how it did not take hundreds of years for their divine origin to be accepted and believed. It's quite remarkable.
There were many, many Jewish texts available in the first century, which were not later included by the Rabbis. The Rabbis finally settled on the general standard that the texts had to be in the Hebrew language. But though the Pharisees were their precurors, we do not know exactly which books the Pharissees scholars commented. The Talmud tradition developed after the final desecration of Jerusalem. The three fold division of law, prophets and wisdom is too vague to justify your claim that the Jews of Palestine used the equivalent of what we call the Old Testament today. Further, we do not know what the role of Jewish books in Greeks played in the Judaea of Jesus’ time. The simple fact that we call Our Lord by the Greek form of his name, that the New Testament is written in Greeks us how much variation in the Judaism of that time.