Last part first: you're right. I meant CRT RPTVs don't have a native resolution. DLP, LCD, and Plasmas all have a native resolution and whatever that resolution is is what you should set your PC resolution to.
I have heard that you can fry your TV if you send it a "bad" signal. Having said that, I sent my TV all kinds of bad signals before I figured out what I was doing and it still works just fine. I've also heard, and I figure this is probably the bigger reason, that TV manufacturers didn't want to deal with the tech support issue of people calling in to say their TV is broken when it was actually a settings problem with the PC. I think that's pretty much been solved at this point now that nVidia and ATI are including 16:9 resolutions in their drivers. Before you had to use Powerstrip to force the video card to display what you wanted but with just a few exceptions for the occasional odd resolution displays, Powerstrip is no longer necessary.