The tournament golf analogy is false because the players are not playing against each other - they are playing against the course, in parallel with each other. Competitors are not able to call penalties on competitors who are not in their group. That's a big part of the reason why Rule 1 in the USGA rulebook states:
It is literally Rule #1 in golf that you are required to call penalties on yourself.
As far as I know, there is no such rule in pool.
Match play golf is the closest analogue here, and in fact there are times when a player has no recourse for failing to fall a rightful penalty:
"A player can not wait to report a violation after the players have gone to the next tee either. That once happened in the Ryder Cup when Ballestoros noticed one of the American players had played the wrong ball in the alternate shot format. Ballestoros failed to do it when it occurred and therefore the claim was not allowed."
http://theaposition.com/jamesamcafee/golf/270/rules-different-for-match-play
Perhaps Barretta should have volunteered the information that she had fouled, but that contention seems far from clear cut.