'embedding' is more than simply linking; I'd suggest that it's pretty close to publishing. That may not mean you need to actively 'police' your site.
But it almost certainly means that you need to act on complaints by copyright owners (or their agents).
In practice, it's only sensible: if they are chasing you, they are almost certainly going to chase YouTube etc., as well - making your embedding look pretty silly.
BTW, I'm not a lawyer etc., etc...
