Allow me to be a contrarian regarding the "benefit of the doubt" thing.
I always complain in the NBA when the refs call the game differently in the minute of the game. For instance, when Brent Barry was fouled on the last play of the game a couple years ago in the playoffs, and the official swallowed his whistle, many of us complained.
Isn't it the same situation here? If the ump thought the guy was out, he has to call him out, even if it's the last out of a potential perfect game. I commend him for making what he thought was the right call, because it takes guts to do that. I also commend him for having the character to admit his mistake, and for genuinely feeling bad about it.
Of course the call was wrong, and that sucks. However, it happens. Even though he looks clearly safe on replay, that's still a bang-bang play to the naked eye.
I agree, and was thinking of a way to articulate this earlier. It's not a bad call because of the context or what could have been. That's why it's news worthy, but not why it was a bad call. It's a bad call because he was out and was called safe. It would have been the same degree of bad call in the 5th inning of a 9-5 game.
Additionally, it was a failure of this ump, but was not his fault; he's a human hired to perform a job at the best of his ability. The Failure is with the league that has the technology, money, and power to change how calls like this are made and reviewed. It indicates an institutional failure.
If we are that worried about inevitable bad calls ruining historic moments, MLB could easily say we will have booth review (honestly, it takes about 30 seconds, or half the time a typical pitch takes, to see 4 quick replays in HD and make the right call) for: foul or fair balls; home runs; and safe/out calls in the last three innings of a. games closer than 3 runs, b. no-hitters, c. perfect games.
Simple. Low impact. Done.
As a basketball aside, I HATE the idea of "let them play" in the last minutes of a game. What??? It's completely illogical: different, malleable and changing rules within the same game?!?! How is that a sport? The whole point of a sport is that there are standard rules of fair competition throughout the entire length of the contest, to the most accurate degree possible. A rule is a rule, and it doesn't matter when you break it; a bad no-call is just as "wrong" as a bad made-call.