I don't think point 2 is that we have evidence that rape had occured. Rather, the (intended) claim was that even when a rape occurred, the evidence available would amount to he-said/she-said.

I read "absolutely" in this to exclude cases where the question is not one of facts, but of definitions. Eg. if the victim was somewhat intoxicated, both sides can agree exactly on the facts of what occurred, but disagree if the victims consent was valid.

"Rape Kits", or rather, the standardization of process for collecting evidence after a sexual assault, are surprisingly good at collecting usable (convictable) evidence after a sexual assault.

The biggest problem with them is that roughly half of them go untested. When they are tested, however, they're actually incredibly good at the successful prosecution and conviction of sexual assault cases.

When the rape was reported soon enough for evidence to be collectable; and when it was a form of rape that leaves a distinctive mark relative to consensual sex. I do not know how prototypical these both of these conditions are; but at most, you would reduce the "usual" qualified to "non-negligible", as there certainly are cases that do not meat the criterion to have a usable rape kit.

(Unrelated note, in writing this comment, I tried looking for relevant statistics; but found I have no idea what to even search for. Anyone have anything?)

Sure they can. It can be possible for a rape to have occurred, but for there to be no evidence beyond the victim saying so. That's the most usual case, and why dealing with rape is so hard.