If somebody owns something, it's not mine to take from them, even if I want it really badly.
On the flip side of the conversation, if someone posts something on one of my websites, it isn't my place to tell them "No, you can't do that". The only exceptions to that are for obviously spam messages and attempts at breaking the site (whether phishing, hacking or whatever).
The easy answer for me, that I made long ago, was to just not allow self-image hosting, which at least defers some of the harder decisions to somebody else, and thus far has saved me from having to deal with lawyers or cops, except for one situation, which was... awkward.
Thankfully, I haven't run into any issues of plagiarism to my knowledge, because those would be obviously infringing, and I wouldn't be able to pass the buck to anyone but me.
Edit: Oh, and thanks. That was all I meant to type originally, but for some reason, I'm exceptionally wordy tonight.