Caching is parroting what the original poster publishes. If the OP asks not to index, you cease indexing. However, if you are purposeful "hosting," you may not accept and continue hosting, knowing all the legal consequences that may follow.

Caching has nothing to do with indexing. If I set up an HTTP cache to serve cached websites on my network, it would be difficult for anyone to request to not cache the HTTP responses considering it is most likely they would not be aware of them at all. It is, however, exactly equivalent to what websites such as archive.ph are doing.