Simpleton is no fool. All schools expect that you are applying to other medical schools and the fact of them being in the same town is irrelevant. However, a possible contributing factor to this PERCEPTION of a BU-Tufts rivalry is that, while BU has 135 openings for its first-year class, no more than about 70 are offered on the open market. Why is this? About 45 seats are taken through formal commitments to BU's combined BA/MD and other special programs with their undergraduate school. About 15 of the remaining spots are also usually offered to BU undergraduates or from cooperating institutions. Thus BU might appear to be rejecting many applicants not in these categories who may also be applying to Tufts. I am NOT saying that there is no BU-Tufts rivalry, although I doubt there is, but that alternative hypotheses might explain the perception.
For folks intending to be physicians, it is important to develop the habit of not jumping to conclusions without consideration of other possibilties, unlikely though some may appear, to explain phenomena. Indeed, that trait often distinguishes the best diagnosticians and scientists from the run-of-the-mill.