People with stutters can sing?

American idol is on my tv in the background.
Some Latin American guy with a great voice has just been singing a Beatles song.
After he’d finished, the judges were talking to him and he had one of the worst stutters I’ve ever heard. He really struggled to get his words out, yet could sing perfectly.
It’s not the first time I’ve come across this phenomenon either, but it always makes me wonder… Why is this the case?