That is why you can find their catchy songs on any Jukebox in the world. You got their "founding year" wrong. It was more like 1962 with their first America album released in 1964. This is off the top of my head, so I could be wrong. I believe the album was, "Meet England's Newest Hit Makers. The Rolling Stones." All covers except for one original I can't recall.
Here's an anecdote. In 2002 (or so), I went to a Bo Diddley concert. Or should I say, a Bo Diddley rambling. He told a story of he and his sister going to England to be with the Jagger, who liked to learn from blues legends and others to learn directly about their craft. Jagger didn't just copy them, he learned from them and performed with them. That's why I consider him, with influences like early rocker Tina Turner, the genius behind classic R&R.