No, your logic doesn’t follow.
Let’s say you & I both say our favorite musician is Mozart.
But when we both listen to pieces, you are able to correctly identify the name of the piece, what it was written for (ie for Mass, an Opera, etc) and I consistently get everything wrong does that mean that Mozart isn’t my favorite musician?
No. It simply means that you know Mozart better than I do.
It’s the same with the Muslims because they say they worship the God of Abraham. The Jews, Christians & Muslims all profess to worship the God of Abraham, and it’s true that we all do. However, we have a different understanding of who He is.
Now, the same thing could NOT be said about the Buddhists for example because even if they said they believe in the one true god, they would say they do NOT believe in the God of Abraham.
The one true God is the God of Abraham.
Furthermore, the Muslims actually beleive in the Virgin Birth of Jesus. The Muslims rever Mary.
From my point of view, Muslims do beleive in the One True God, however, Islam is really another of the great heresies - a greater heresy than Protestantism.
I pray this makes sense.