I would suspect that all (mostly) self-reported statistics like that have problems.
I recall that in college we would have course evaluations near the end of each course when we were asked things like "How long did you spend studying for this course each week?" and a set of 4-5 fill-in-the-circle answers. I never kept track, so I usually just made up an answer (that I hoped was reasonable).
Questions about self-reported binge drinking may have similar problems. (One of the side-effects of binge drinking is loss of memory...). And you're right that there are all kinds of reasons why rape and sexual assault statistics may be suspect.
Any sexual assault is one too many. The way to address it, though, needs to be more than telling women not to go to parties with alcohol and having more rape kits available. Kasich's approach won't solve the problem or even reduce its prevalence because it doesn't address the reality. (The reality is that too many young men think that women exist for their benefit and don't understand (or refuse to recognize) that women are independent people. That's what needs to be addressed from a young age, and especially when people are on their own for the first time.)
My $0.02.
Cheers,
Scott.