Yes, actually, those odds DID have something to do with that. The 1 in 278 million is a mathematical combination of 4 separate statistical probabilities. The real numbers are certainly different than listed, as they are each based on the ultimate conclusion of the previous, but the odds would still be nearly the same.
Those odds are predicated on the first probability - that the Sox would give up a 9 game lead and miss the playoffs - a 0.3% chance. The percentage probability that they would give up that lead and be one strike away from forcing a 1 game playoff is negligibly higher than 0.3%. Same with the Rays getting to within 1 run after being down 7-0 in the 8th inning.
What is being said here is the chances of the Red Sox blowing a 9 game lead, then being within 1 strike of winning their final game and ultimately losing, AND the Rays coming back from 7-0 to be within 1 run in the 9th, then tying the game AND then winning it - the chances of those 4 things happening is 1 in 278 million. Yes, that is believable.
One problem. When the Sox were one strike away from winning, the Tampa Bay game was already tied. The Sox/Orioles outcome was always in doubt as it was a close game throughout. As to the 1 in 278 million, who gives a flying duck about those permutations. Bottom line is the Sox played horrendous down the stretch and deserved their fate. Btw, anybody hear from sinkhole lately?

Pretty sure I didn't bring up 2004. Yet "we've moved on...". LOL