True. It also brings into question why the Muslims say they accept the Jewish and Christian scriptures. Clearly, what they mean is they accept their own versions instead. I've read the Koran, and I've read the Bible, and in the Koran, it has the Jewish prophets saying different things than they do in the Bible. Um, wait a minute... (scratches head)
As far as I understand, Muslims accept the Jewish and Christian scriptures as "Word of God", but believe that Jews and Christians have altered them to suit their own ungodly purposes. Therefore, any scriptural passage that does not comply with their beliefs, they believe it to have been altered. Only the Koran is believed by them to be the unaltered, and therefore purest, revelation of God... a kind of "ultimate restoration of the original faith".
This is their belief. My conjecture is that, during his lifetime, Muhammad met only Christians from heretical groups, and never got to know "mainstream" Christianity. Therefore, any Koran story that retells an OT or NT story, or any opinion on Jews and Christians written in the Koran, is distorted from the origin.
I have read about half of the Koran. I left it before finishing it, because it was dense and repetitive to read. What struck my attention is that it was written in a very defensive attitude: every now and then, it repeatedly states "this book is the Word of God", as if the writer was unsure and had a need to assert it. As far as I know, nowhere in the Bible we can find the statement that the Bible is the Word of God... it is implicitly assumed, but not stated. It also repeats its promise, now and then, of sending to Hell everyone who is an "infidel" (i.e. not Muslim), and rejoicing in it. It doesn't speak about having balance in the Final Judgement, judging sins... having faith in Islam or not is the only divisive line between being sent to Heaven or Hell.
I may be oversimplifying in my opinions, and may have got some stuff of the Koran wrong. I will be happy to stand corrected. Still, I cannot say if they worship the same God or not... God may be hearing their prayers after all. But I do think that God, as portrayed in the Koran, shows a personality that we Christians would not recognize in our God.
If the stick defining whether God is the same or not is to look for a Trinitarian belief, then I don't know either if the God of the Jews is our same God... current Jews don't believe in the Trinity... they dismiss that idea as "refined polytheism".