Tinker
Because they're icons in the sport. Not necessarily saying I agree with it, but this is the way most Captain's picks have gone in the past. Phil and Tiger, as much as their respective games have deteriorated over the past couple of years, are still huge draws in regular tournaments. There's proof of that.
So imagine how much their presence factors positively on viewers during Ryder Cup, regardless of how they perform. People are gonna tune in to see how everything unfolds.