SOLVED -- Switch PIN, Also Trigger Other Pin in Arduino
You may be getting switching noise between the button wires, which is low-level and brief, but with no debouncing, it could be just enough to cause the effect you're seeing.

I'd suggest 1) writing a short function that debounces and reads any button; and 2) using if/else statements instead of testing each button twice.

A quick test is to hold one pair of wires closer together or farther apart from each other while you press one of those two buttons, and see whether the distance apart changes the effect. If it does, you've found the cause.