No, it means one of us is factually and historically correct and one of us is completely delusional and dishonest.
If I came along and tried to tell you that Thomas Jefferson was really a Communist, would I have a legitimate argument? What if I could support this idea by re-writing history and historic events, and portraying them erroneously? Does that make the idea more credible? This is what you are arguing on behalf of Islam, that their teachings and religion are based on the same concept and understanding of the same Abrahamic God, and that is false. They have a completely different understanding and perception of Allah than Christians and Jews have of God, and it's based and rooted in a false portrayal of events in history and lies about documented historical events.