Yeah, I thought I could go a different way with that but in light of the equal product distribution it was an incorrect starting point. I'm going back to the "this is actually a trick question" statement. Your reasoning is sound, but there's something else happening here which is honestly beyond the first few weeks of an o-chem lecture.
Again, I recommend that you look up the cyclopropylmethyl carbocation and the cyclobutyl carbocation. They are different from other carbocations.