Bale was thought to be the first name on Stuart Pearce's team sheet for the Games but withdrew from consideration earlier this month with a back injury.
However, before Team GB have even kicked off their opening group match against Senegal at Old Trafford, Bale was involved in his club side's pre-season friendly against the MLS side.
It has a move that incensed FIFA president Sepp Blatter, who called for the player to be banned from all football during the Games.
But BOA chairman Colin Moynihan insisted he was laid-back about the situation.
"I don't agree with Sepp Blatter's comments," said Moynihan. "I'm just pleased that Gareth has returned from injury quicker than expected."
Team GB chef de mission Andy Hunt also refused to fuel the argument ahead of Thursday's opening match in Manchester.
"All I would say is that Stuart is very comfortable with the team he has and we're looking forward to them starting their first match," he said.
"Stuart made his selections based on fitness and form, you can't predict a recovery period from an injury.
"Gareth's missing an amazing opportunity which I'm sure he will look back on and be tremendously disappointed about."
The Team GB squad without Bale: