Getlo is correct. The only people who originally claimed this were the record company and Elvis' circle. It is from there the myth grew and anytime this is mentioned, the myth is fallen back on.
Total viewers, maybe 1.5 billion, but this was not the number who actually saw the show live, not even close. I think the live numbers are probably closer to 100 million. The next day the rest of the world tuned in (not live) and then 3 months later the U.S. finally got in the game.