How much of "wasabi" is actually wasabi in the United States?
The vast majority of wasabi in the US is mostly horseradish.

Some brands like this one, contain no wasabi at all. That one is the #1 seller on Amazon.

Other brands, including this one, contain a small amount of wasabi, presumably just so they can put wasabi on the list of ingredients. Incidentally, that brand is made in Japan.

Real wasabi can be found without too much trouble. This brand is in the powdered form, you can also get it in a tube. I understand that real wasabi loses its heat very quickly after being grated, which may explain why I actually prefer the fake stuff. I've tried real wasabi in a tube, and I found it disappointingly mild. If I ever see a fresh wasabi stem I will buy it just to satisfy my curiosity. (Originally I called it "wasabi root", the wiki article linked to in the OP tells me it's actually a stem. Hmmm, learn something new every day.)

I have read that most of the wasabi in Japanese sushi bars is the same stuff we get here. Even in Japan, real wasabi is the exception, not the rule.

You bring up an interesting point about the legality of labeling a product "wasabi" when it doesn't contain any real wasabi. Our labeling laws usually wouldn't allow that. My guess is that it's a loophole just for wasabi, maybe written especially for Japanese exporters. 

HA! There is even an on-line petition to ban the practice of labeling horseradish "wasabi".