Calling Kenny G, The Rippingtons and most similar stuff contemporary jazz is kind of like calling cool whip and velveeta cheese modern cuisine. Contemporary players like Dave Holland, Tim Berne, Fred Frith, Gerry Hemingway and Ken Vandermark get a fair amount of respect, (but maybe not a whole lot of $$$). Going back a couple of posts, it could be argued that blues and a few of its evolutionary mutations have American origins. Instrumental surf rock per the Ventures, The Mermen, Los Straitjackets, Link Wray and Dick Dale for example. Sorry if this is getting a little too off topic, but another huge uniquely American figure (whose recent death has been puzzlingly overlooked on this site) is Don Van Vliet (Captain Beefheart). He put out records with percussive elements and phrasing that you can't pin on anyone else and he influenced a heck of a lot of other recording artists.