Just for posterity, the secondary appeal was to a 10-person committee. 2 couldn't attend and a third recused himself as a former principal of one of the schools. The remaining 7 voted on the final appeal. They ruled 5-2 in favor of Johns Creek, overturning the ruling on the field and the results of the first appeal. Thus, Johns Creek was declared the winner 4-3 and a third game was played (which Lee County ended up winning 8-0).
There was no official reason given for the appeal ruling, however, at least one of the committee members gave some quotes. Based on those quotes, it appeared that the reasoning behind the ruling was the umpires' judgements, not the rules. That is, they didn't determine that the rules were miss-applied or miss-interpreted. Rather, they said that, basically, the umpires blew the call and reversed the judgement -- the umps said the guy didn't touch 3rd base, but we think he probably did, even though we weren't there. The guy sort of admits that they set bad precedent in going that direction.
I also read that the original on-field deliberation lasted 20-25 minutes and there were reports that at least one of the umpires was consulting a cell phone during that time. The committee briefly stated that no cell phones were used. But, the committee also removed the umpire crew from the remaining playoff games ... which is severe, I would think. Seems odd to give the old "they did nothing wrong; they're fired" statement.
In any case, the committee is right. The next time a playoff game ends on a bang-bang judgement play, they have set precedent that this would be grounds for a protest and appeal. Yikes! Who wants to umpire in Georgia now? ;-)