You may be quite right in you conclusion (!) (!)...
... and yet it cannot be "simple as that." If it were "simple as that," we could also say:
"Jews do not believe in the Trinity, therefore YHWH is not God. Simple as that."
"Christians believe in the Trinity, therefore they do not worship the God of the Torah (Old Testament) (Hebrew Scriptures)."
Keep in mind that neither Jews not Muslims are Trinitarians.
Yes - I am aware that Jews are not Trinitarians either, and as soon as I posted I realized that someone would point this out and rightly so!! However their (the Jewish people) scenario is entirely different. Of course YHWH is the true God of the trinity, even though Jews don’t acknowledge the trinity, that doesn’t make it not so.
Jesus was Jewish. YHWH is His Father, and furthermore YHWH specifically announced to all that Jesus is His son at the time of Jesus’ baptism. Since the God the Father of the Trinity is exactly the same as YHWH (they are the same Being) then there is no problem.
A great difference is that Jesus is a Jew, and king of the Jew, who came fulfillment of the Law of Moses. If we take as true that Ishmael is the father of the Arabs, Abraham was the father of many other nations, but Jesus belongs to the nation of Israel, through the root of Judah. and a descendent of David,king of the Jews and then all Israel. There is a history, but the line of Ishmael cannot be traced. If Mohammed believes in the God of Abraham, he believes in the God of the Jews. But he may, in fact, believe in the chief God of the Pantheon of Mecca, whom after the Hegira, he identifies with the God of Abraham.