One of the underlying themes of sabermetrics is the human struggle separate our emotions from our perception of reality. A player dropping a key pop-up that costs your team the game does not automatically make him a bad defender, no matter how angry you may be with him. A player coming through with a pinch-hit, walk-off grand slam doesn't mean he has some inherent clutch ability, no matter how elated you may be with him.
Emotions often obscure reality by bringing excruciatingly painful or blissfully positive memories to the forefront, whether the moment is repeatable or not. We are all prone to discarding the the overwhelming majority of the data when our emotions are involved, choosing instead to follow the skewed perception down the rabbit hole before realizing it is nothing more than an illusion. Human emotions are a very, very powerful thing, powerful enough to strip even the brightest of baseball men of their objectivity.
A bullpen meltdown may be the most frustrating type of loss in baseball. Not only should the game have been won (in this case, the Blue Jays had a 99.5% chance of winning heading into the bottom of the 7th), but the failure is systematic (four Blue Jays relievers combined to retire only two of the nine batters they faced in the 8th inning). The Blue Jays reacted to this ugly game by designating David Purcey for assignment. An action bred in frustration is an opportunity for another party; Billy Beane saw this and acquired Purcey for Danny Farquhar a week later.
A month went by, Purcey appeared in 9 games for the A's, posting a 2.13 ERA in 12 and 2/3 innings and limiting opponents to a .538 OPS. His peripherals suggested bad regression was on the horizon, but it's hard to say Purcey wasn't effective for the A's. He had re-built some of his former value. Then Beane struck again, this time shipping Purcey away for another player whose former team was making a frustration based move. Scott Sizemore, owner of a career .300/.388/.453 triple-slash in the minor leagues (.314/.396/.486 at AAA), had been given all of 237 major-league plate appearances to prove himself with Detroit's big club. He hit only .223/.306/.306 in those 237 PA's, but given his minor-league track record and affordability, Sizemore is a commodity that carries a lot more value than a 29 year old, hard-throwing, left-handed reliever without a reliable secondary offering.
Starting with Danny Farquhar, Billy Beane identified two players whom their organization had given up on for emotional--rather than objective--reasons and ended up with Scott Sizemore. That is basically why Beane is one of the best in the business. Regardless of how this trade turns (I expect it to end up looking very good for the A's), the process was unquestionably sound, and more times than not you'll win by doing what Beane did.