The relationship is: Linking >>>> inline'ing > copying.
http://www.chillingeffects.org/linking/faq.cgi

Linking is by far the safest. It has been tested in court and the courts have said it's simply speech, with all the usual freedoms (i.e. SLAPP in some states). The exception is when the site's all about infringement, such as PirateBay. Lawyers would discourage their clients from suing over a link. Good chance you could get a lawsuit chucked early.

Inline (embedding an image from another site) or framing (embedding a whole page from another site) is not copying. But first, it leaches bandwidth as discussed, and second, lay people have trouble distinguishing it from copying, so may drag you into court just the same. And since the distinction would be lost on lawyers and judges as well, you'd have a lot more trouble getting it chucked out, and would likely have to go through the grind. This is almost as bad as losing.

My suggestion: If a user is inline'ing, and you get a DMCA takedown notice for that content, remove it!

And - like robertjohndavis reports - if you have any copied content from news media, kill it on sight. Convert it to links to that content. Even if it was posted by site members. DMCA Safe Harbor doesn't protect a BBS if they knew about the infringement. It also doesn't protect them if they haven't registered an agent with the Copyright Office. http://www.copyright.gov/onlinesp/