In fact, they hired him before Moneyball came out, privatized his research and are essentially the ONLY people that have been able to read him for much of the last decade.
I got to go to what seemed to be a rare Q&A with him last year, and it was pretty f-ing fascinating. He talked at length about trying to statistically evaluate leadership, chemistry, fights and catching defense contribution.
As for the Yankees, there was an article recently that said something to the effect of "it's not just the size of the payroll, but their ability to spend it wisely which scares other teams".
The Rays were like that, until they got a new owner and dumped pretty much their entire front office right before 2006. Their best 2 seasons have been the last 2, with Andrew Friedman as head of baseball operations, and he's regularly lumped in with the moneyballers (his focus has been strong defense, something that hasn't historically been valued as highly as offense).
Also I found that the article's point that the A's success was largely due to 3 20-game winning pitchers to be fallacious. Wins by pitchers aren't really a useful statistic.
The old guard will do anything they can to discredit sabremetrics so they can go back to the old ways of folklore.
However, I think your example is "cherry-picked" in iteself. The Rays finished only third this year, and in their whole 12 year history finished in dead last 9 times... mainly because they did not have the money to compete.