One of my first choir directors did his Masters thesis on people who "couldn't" sing. As part of his research he assembled a group of such people and, after much hard work and some one-on-one tutoring, formed a choir of these people. The choir eventually performed songs before the entire university population!

IMHO singing on pitch is not something one is born able to do. It is a learned process. It requires practice. I grew up singing along with my little 45 RPM records of Disney's "Johnny Appleseed" and a Sons of the Pioneers recording, among others, as well as singing with whomever was on the radio. Some might say that I eventually got it right.

People who can't match pitch haven't given it an honest try.