Applying to Cambridge, would this realistically affect my application?

I'm applying for Nat Sciences at Churchill College. One of my teachers told me that someone else at my school is also applying for the same course and the same college, and if I believe if it'll affect my application I can change what college I want to apply for. I have no idea who this person is and if they're a better suited cambridge candidate than me. I was really settled on Churchill, so should I rethink colleges? I know it shouldn't affect my application in theory, because they're supposed to treat us equally, but in practice, would this turn out to be a problem?