The Grammy award winning band refused to license their popular music for the use of the hit dramedy show. The reason behind the refusal? The Kings are determined not to “sell out.” But there are no hard feelings toward the show itself; Followill added that even though he’s never seen an episode of the musical TV show, "apparently everybody loves it."
Followill continued to say:
We had some people call us up wanting to know if we’d allow ‘Use Somebody’ to appear in the trailer for their next movie, and we turned them down. Next day, they called back and tried to put us through to the star of the movie — I won’t name names, but he’s an incredibly famous actor — to let him try to convince us to agree to do it. I was like, 'Man, don’t even waste your energy.’
Hard to get at what the real reasoning is behind this. I'm pretty sure the "sell out" part is something added by the blogger and not an actual quote from the band. It's been pointed out elsewhere that they allowed their music to be used on Gossip Girl.
So maybe it's just this one song that has special significance to them? Or maybe they think a Glee cover of this particular song is a horrible idea?