Yes, given that my employer can decide to dismiss me with zero warning, I don't really feel a blanket obligation to give them any more warning than I'd expect them to give me (i.e. zero).

I would give warning to my current employer, because I've been here for a long time, they've treated me alright, and I have a lot of knowledge that's important to the business. But I'd see it as a courtesy, not an obligation.