You have the statement wrong, it should be
"If Americans care about a sport then they become best at it."
You see this is how that works. We have the viewing audience with the most money and will buy the titles via the best players if we care. Most of the time "care" is determined through marketing.
Here are the 2007 muscle ranking for sports money
tiger
lefty
beckham
Raikkonen
James
mayweather
ronaldinho
messi
bryant
federer
alonso
oneal
Out of those earners 425 of the 580 million dollars brought in was american.
My point is we care because that is what is marketed to us, not what we really care about. With that said the marketing doesn't work if we aren't the best. If you are going to spend a lot of money to cheer for a good team or player then it/they better be good for the money.