I was just about to mention MMW.

Great band who is certainly more jazz than Rock. I just think the term is a little more specific than "bands who are known for improvising" The whole cultural thing has a lot to do with it, I think. The same people who followed The Dead from concert to concert are the same people who follow Phish and WSP. Its a very tight-knit hippie, music festival thing.
And while I agree, it really could be a band from my genre, it's more popularly associated with the things I was saying above.
Another thing to factor in is how many bands welcome the title "jam band"? I think nearly any jazz band would prefer to stay away from that title. Theyd probably think it was somewhat derogatory. Even Gregg allman has said he'd rather be known as "a band that jams". Members of WSP have also been quoted as saying they wanted to Lose that title.