[kemayo]

User-provided content is provided under a license between the user providing it and the site hosting it -- inherently, because otherwise the site wouldn't be allowed to do anything with it at all. Generally this takes the form of the site's ToS saying that the user gives the site a perpetual license to use the content however they want, but generally not an exclusive license.

As such, and I'm not a lawyer and can't promise this is true, I suspect that reddit couldn't actually do takedowns on someone who's archiving their user-provided content. Any specific user whose content was archived without their consent could do so, however.