Here's what happened with Brunell: Brady said that he is very particular about the balls he selects, he wants them at exactly 12.5. He tests the laces, he wants the body tacky. When asked if he noticed the difference during the game, he said PSI is the last thing he's thinking about the 30 times a game he goes back to pass, so no, he doesn't notice a difference in those 2 seconds.
Brunell then crunched everything and said he was very particular about the selection of his balls, and knew the PSI exactly, and that no way can Brady make that claim. In other words, Brunell completely disregarded what Brady said about selecting the balls.
As for your other point about Pats personnel handling the balls, no. The balls are given by the refs to NFL paid ball handlers (who are local). For a Patriots employee to do the deflation, he would have to do it surrepitiously because they are not otherwise in their possession. The balls go into a bag on the sidelines that is handled by a person with NFL uniform.