My gut tells me that yes, they do. What's the alternative?

"We're just a platform your honor. We are not responsible for the rape content that we host on our website."

Seems like an unsatisfactory standard.

> Does PornHub "publish" the videos on their site?

Some, possibly not all (especially in a US legal sense, given CDA § 230), but it distributes all of them, and the law applies to distribution.