There's no denying that Tiger had an impact on purses. And not just in dollar figures, but the number of sponsors as well. Companies and corporations were lined up at the door wanting to be a part of the sport when he was dominant, because it gave them enormous exposure.
There was a fairly dramatic lull in pro golf interest after Palmer/Nicklaus were beyond their primes. You had an occasional uptick with players like Watson, Faldo and Norman in the late-80's to mid-90's, but it was far from being sustainable long-term. Then Tiger came. The Golf Channel went from a struggling concept to signing lucrative deals for cable tv programming, almost overnight.
Phil Mickelson knows this better than any of us, since he was there to capitalize on it himself. And when he gives due credit to Tiger for all of the money and sponsorships that have flowed into the sport since that time because of his presence (which he has done on numerous occasions) I don't think he was talking out of the side of his mouth. He was being sincere. Tiger might be a rival of his, but he's also part of the reason why Mickelson has bankrolled a lot of capital over the years.
Palmer and Nicklaus played an enormous role in bringing the game to the public via tv. They popularized the sport to viewers, and sure... that added increased interest to sponsors.
But to overlook the influence of Tiger is just ridiculous.
Look at the numbers of the television ratings the last couple of events he's played, versus prior to him returning.
It's rather significant. He attracts the casual viewer, whereas Spieth, Day, DJ, etc. only attracts the avid viewer. And the sponsors know this. And they've known it for a long while.
The sponsors aren't just out there trying to market to the avid viewers who already tune in. They're also looking for those who don't tune in. Maybe even more so.