I also imagine that only psychopaths actually rape.

Don't think that, unless in so thinking, you also think that "a psychopath" can be a functional, indistinguishable member of society who you'd never once know even through extended association unless he happened to tell you about that one time at that frat party (or whenever).

Completely correct. I speak not just from reading about it, but also from knowing one woman (that I know of) who was assaulted and the case quite clearly did not involve psychopaths. It involved a gang of ordinary teenage boys egging each other on when she was in their power.

Rape is (statistically) normal human male behavior, and is not correlated with any diagnosable psychological or physiological condition that I know of.