I don't know whether to be scared or reassured reading all these posts.
Here's what I decided to do. I got under the RV and washed it, just soap and water, so I could see the state of the rust better. (Got a nice bath myself.) Mostly it appears the rust is superficial. There's one place on the front that appears to have a bit more rust.
I'm going to put rust remover on the tank, covering as much as I can, wash it off. Let it dry and paint it with silver paint. (I think one of the first responses suggested this, so thanks.)
As a precaution, the next time I drive it into town (I'm quite a ways out), I'll stop at the RV place and have him look at the fittings and hoses. Anything that looks sketchy will be replaced.
That way I think I've covered all my bases. And here's a tremendous shout out to all of you who gave such wonderful advice.