Credit card companies should not have this kind of power

When it comes to pretty much anything sex-related, consent needs to be provided, not assumed. If consent has not been provided by all participants in a given porn video, you cannot assume that you have consent to distribute it.

The issue was not that the removed videos depicted rape. The issue was that it was impossible to verify that the participants consented to having the videos distributed. If the rape depicted was fictional and nothing illegal happened? Great. Big fan of people not getting raped. The site still didn't have consent from the participants to keep them up, though, so they took them down.

Perhaps not directly, but copyright played a role. Broadly speaking, the user verification process allowed users to confirm that they have a right to distribute the content they upload. For amateur or self-produced stuff, that means the user has to confirm that they represent the participants and can provide consent to host the material, which is pretty intuitive. For commercial material, though, the participants signed over that consent to the production company, establishing them as their representative for the purposes of consenting to distribution. That means it's the copyright holder's consent that's needed to distribute the videos.

In the case of videos with no participants that need to consent (animated stuff, mostly), the consent of participants obviously isn't relevant, but the account verification process still requires users to prove that they have a right to distribute the videos they upload. Unless they are themselves the copyright holder, though, they can't really do that, so the videos get taken down due to a lack of the copyright holder's consent. It's not explicitly a copyright claim (stuff can get taken down for that reason, but that wasn't what happened in the purge in question), but it effectively amounts to taking it down for copyright reasons.