The Muslim perception of Christianity is defective, in the first place.
However it happened historically, the Muslim understanding of Christianity is from the point of view of the Arian heresy – that Jesus was just a man, not God, and did not die on the cross.
So, with that preconception, they’d naturally believe that the Bible (NT in particular) is corrupt.
Faulty assumption leads to faulty conclusion.
I can’t think of the Catholic apologist of a century ago who described Islam as an external heresy of christianity. (who was this? can’t think of his name)
Muslims accept many Judeo/Christian beliefs, but (significantly) they seem to have rejected the inconvenient parts of both. That’s why it is a heresy. It grew up outside the synagogue or Church, that is why it is an external heresy.
On the following point, I may be confusing mormonism with Islam: I think both the Book of Mormon and the Quran have been re-written to resolve problems that were found in them.