And I'm listening to all kind of mellow covers (airport music) of Led Zeppelin, Eagles, Stevie Wonder - this is bad taste
Of course, they don't play the original tunes, because a) it's cheaper and b) it would be intrusive.

Question: did Allen klein or the Stones sell any kind of copyright for that cheap airport music/ musak?

Well, in fact yes: they are playing a terrible disco version of Angie. No joke.

<<did Allen klein or the Stones sell any kind of copyright for that cheap airport music/ musak?>>

Any type of cover for public consumption would result in songwriting royalties for Mick and Keith, performance royalties for the Stones, and publishing royalties for ABKCO (pre-1971). But no licensing deals would be required if just musical covers--those deals involve TV commercials and movie rights and the like.

Here's a cover that would give Muzak a run for its money: Complicated by The Ukulele Orchestra.