There's alot of fuzziness out there, with lines blurring in country, alt-country, folk, rock and blues.
Hem's folky alt-country really. Steve Earle's rock country. Solomon Burke is R&B country on some of his albums, when he's not straight R&B or blues.
Bad Livers, like BR549, are straightup shitkicking country. Great stuff!
By that criteria I would have to add Lambchop. Kurt Wagner is a genius, IMO.
My favorite term is "Y'allternative"
In the old-school bent, I've been listening to The Sundowners, a band that held court in a basement dive bar in Chicago next to the Greyhound station for something like thirty years of five-nights-a-week shows.
Most of the tracks were recorded live in bars over the decades, complete with beer mugs clinking in the background. Seriously real deal.