You are referring to Talmudic sources. They are not historical and not reliable.
This guy is an historian and reliable.
Solomon Zeitlin: During the Second Commonwealth there were no synagogues as houses of prayer in Judea. The word synagogue does not occur in connection with prayers in the literature of that period.
Upon discovery of the Dead Sea Scrolls in the 1940s, he questioned their authenticity and used methods to do so that resembled the field of public relations more than scholarship. Some of his claims have no basis in fact whatsoever, and should be treated purely as speculation.
So he is in a minority of one who argued the authenticity of the Dead Sea scrolls.
This is disproved easily, as Philo, who died before the destruction of the Temple, and Josephus, who lived through it, report the tradition of the synagogue as a house of prayer:
"Another Greek name for synagogue in use among Hellenistic Jews, is proseuké, shortened after the analogy of sunagogé, from oikos proseukos, house of prayer (cf. Philo, "In Flacc.", §§6, 7; "Ad Gaium", §§20, 23, 43)."
"The Latinized proseucha of Juvenal (Sat., III, 296) means the Jewish house of prayer or synagogue. Josephus (Antiq., XVI, vi, 2) cites an edict of Augustus which calls the Synagogue sabbateíon, the Sabbath-house."
http://www.newadvent.org/cathen/14379b.htm
From the same link:
"The Jerusalem Talmud (in Ex., xviii, 20) dates it from the time of Moses; so, too, the tradition of the Alexandrian Jews, according to the witness of Philo, "De Vita Mosis" (III, 27) and Josephus, "Contra Apion." (II, 17)."
Even if one disputes the Jewish tradition that the synagogues always existed, one cannot dispute that they existed as "houses of prayer" prior to 70AD.
In response directly to Zeitlin:
"[I]t would be misleading to claim with Zeitlin that the synagogue was originally "not religious but secular," for we now realize that in such a traditional agrarian society our modern distinctions of "religions" and "political" and "economic" dimensions of life were not yet specified, let alone "institutionally differentiated." Thus, as Safrai states, the synagogue was "the people, the community, the congregation and the place where they assembled" to conduct community affairs... or reading of the Torah." (Evolution of the Synagogue: Problems and Progress, http://books.google.com/books?id=lY8yupzDeJwC&pg=PA55&lpg=PA55&dq=Solomon+Zeitlin+synagogue&source=bl&ots=cK9Cl1nK3N&sig=WLyS-pHkcGPf5jQKKrcpIPHg6Bg&hl=en&sa=X&ei=IdfzU8HyOoeG8gGjrIDIAg&ved=0CDUQ6AEwAw#v=onepage&q=Solomon%20Zeitlin%20synagogue&f=false, page 55)