There are many great musicians and instrumentalists among those who improvise music. It is composition on the fly and many times a wonder to behold. Assuredly, not all is good, but much of it is.
There are folks calling certain music "jazz" which I would not. But jazz is a way of approaching the performance of a musical composition. It's not necessarily a dated genre. So, maybe it is jazz, just not traditional jazz.
Have I confused everyone?
The stuff that Duke Ellington and his band were doing during the Cotton Club days is as sophisticated as American music gets.
Slim Gaillard (I think from Steve Allen’s show) on piano and guitar. He learned from Duke Ellington in the 1920s and lived into the 1990s.
http://www.youtube.com/watch?v=qphs31yLcZk
Here’s the first part of a first person hosted documentary about his life (unfortunately it ends just before his music career really takes off).
http://www.youtube.com/watch?v=z3MR4rWovro