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John Lennon appeared on the cover of the first Rolling Stone magazine.
google or photobucket
If The Rolling Stones are a "glorified cover band", they certainly are a rich, successful "glorified cover band".
No
Rolling Stones was published on November 9, 1967. The Rolling Stone Magazine was founded by Jan Wenner in San Fransico California. The main purpose of the magazine is to cover recent musical and political news. The magazine is now known for fan reviews and its strong liberal bent.
The Rolling Stones themselvesMick JaggerKeith RichardsBrian JonesBill WymanCharlie Watts
The members of the Beatles have been on the cover of Rolling Stone the most times. Either as a group or as individuals, they have been on more than thirty covers. The Rolling Stones, ironically, come in a distant second.
I'm unsure, although I think it would be safe to assume that the original lineup has been on the cover, even if it was after Brian Jones had died or even when Bill left the band.
Connection
she felt like it
They didn't
Excellent question! As it happenes they did make the cover of Rolling Stone magazine, on March 29th, 1973. Three months or so after their song 'Cover of the rolling stone', was released.