Don't bother flagging it. It's not a moderator's job or even the site's job to enforce 3rd party agreements. If someone wants something taken down, they need to file a DMCA request.

I'm no legal expert, but saying copyright infringements are always someone else's problem sounds like incredibly bad advice.

Sure the "safe harbor" stuff and the disclaimers in the usage policies make sense. They're there to cover SE's back, and that's reasonable enough.

However, leaving content that's blatantly infringing copyright or redistributions licences (assuming we're above a quantity that's beyond fair use) does no good to the SE community. The main problem is that readers could, in good faith, assume that the user who posted something had the right to do so, and that content could find its way into other places under the SE licensing conditions, where it should never have been in the first place (thereby causing potential problems to the users using that content).

Overall, it is in SE's interest to prevent such problems to happen to its community. Not having a strict legal requirement to do something doesn't mean that you should stay inert. (In fact, that's why most laws appear: because something is not forbidden and then someone goes too far.)

If I go to my supermarket and my car gets broken into, this will not be the supermarket's responsibility (as clearly stated on signs on its car park). Yet, it's not in the interest of the supermarket to let thieves act in all impunity on its car park.