Hmm... So really the definition of a perfect game doesn’t mean that zero batters reached base, which clearly happened in this example?
It's always been my understanding that a perfect game has to be pitched in its entirety by one pitcher, so if a reliever comes in, it's not a perfect game anymore. According to the (presumably accurate) Wikipedia entry, a perfect game also requires that no opposition runner ever even reach first base safely. So, using the entry's examples, if a batter hits a not-quite-double and gets caught at second trying to get the extra base, it's not a perfect game, and likewise, if a batter/runner gets to first on an error, it's likewise not a perfect game even though the pitcher was not at fault, that is, barring the possibility that it was the pitcher himself who committed the error. The entry does mention that this is a revised definition, though, so apparently the restrictions in the past were more lax.
There was a game waaay back in the day. babe Ruth was pitching, IIRC. Anyway, the starter walked the leadoff guy and gets kicked out of the game for arguing. The reliever comes in, the runner gets caught stealing (basically the same as picked off). The reliever then goes on to set the rest of the game down in order. I believe that happened and the reliever got credit for a perfect game.
This too is mentioned in the Wikipedia entry, and by the current definitions, simply counts as a no-hitter, not a perfect game, though it does explicitly state that, at the time, it was indeed called a perfect game for the reliever, Ernie Shore.
Interestingly, the number of perfect games pitched in the modern Major League era in the U.S. and in Japanese professional baseball is the same: 15.
Note that a reliever can lose a game without throwing a pitch, by coming in with the bases loaded and balking in a run.
True, and another interesting bit of trivia, if I'm remembering the rules correctly, would be that the relieved pitcher would get the earned run (since he allowed the runner on base in the first place, assuming he didn't reach on a fielder error), while the reliever would lose the game with zero earned runs.