[chc]

The distinction is very important. The intent of Safe Harbor provisions is not to allow sites to blithely host infringing without possibility of reprisal as long as they take it down when asked. The intent is to relieve sites of the unreasonable burden of both being aware of and policing everything their users do — to allow them to act as sort of a "dumb pipe". If you have personal knowledge of infringing content, you are still expected to take it down even without a DMCA notice — and it is certainly not OK for you to post infringing content yourself.

(Standard IANAL caveats apply of course. I think I have a reasonably good layman's understanding of this stuff since my work touches on this stuff, but you should talk to your lawyer if you want concrete advice.)