They should not do this. A perfect game has a specific meaning: 27 consecutive outs with no hits, no walks, no hit batsmen, no fielding errors. Perfection. There is no room in the rule for an umpire error, even an admitted one. Nor should there be. Umpire subjectivity is part of the game. Baseball has resisted automation forever: there is no instance-replay (as in football), and there are no laser bounds detectors (as in tennis). Once a call has been made on the field and play has continued, that's it. It's official.
This sort of thing has happened before. Wikipedia relates the following (fairly well-known) story:
On June 23, 1917, Babe Ruth, then a pitcher with the Boston Red Sox, walked the Washington Senators' first batter, Ray Morgan, on four straight pitches. Ruth, who had already been shouting at umpire Brick Owens about the quality of his calls, became even angrier and, in short order, was ejected. Enraged, Ruth charged Owens, swung at him, and had to be led off the field by a policeman. Ernie Shore came in to replace Ruth. Morgan was caught stealing by Sox catcher Pinch Thomas on the first pitch by Shore, who proceeded to retire the next 26 batters. All 27 outs were made while Shore was on the mound. Once recognized as a perfect game by Major League Baseball, this still counts as a combined no-hitter.
Shore's feat was no less impressive that Galarraga's. It's not worth cheapening the definition of "perfect game" to include either feat, though. Whether Galarraga pitched a perfect game on June 2, 2010, or not will not affect his career. So it's worth protecting this little corner of baseball lore for true perfection. Galarraga's game will go down in history as a "near-perfect" outing - still worthy of glory.