Coming rather late to the party. Some random thoughts;
The rule seems pretty straight forward as is the requirement for the referee to act on any transgression that they see. In making the decision that the rule has been broken the ref has, in my view, two judgement calls to make. Firstly whether the player picked the ball up before 10 seconds which seems to me to be fairly self evident, and secondly whether the ball was overhanging the hole.
On this second point undoubtedly the person who had the best view of that was the player who picked up the ball. She was adamant that the ball wasn't overhanging the hole although as it appears she didn't know the rule then you could question how closely she was paying attention on that particular point. I don't doubt her sincerity and it appears to me that her reaction and indeed the US players reaction suggested they both thought the ball had missed and wasn't dropping, which isn't the same thing as saying the ball wasn't overhanging the hole.
The unfortunate thing for me in this incident is that during the discussion with the players, the "offending" player having stated that clearly in her opinion the ball wasn't overhanging the hole, that the officials didn't accept that but instead looked at TV footage which at best appears to be suggestive rather than conclusive. At its best golf is about sportsmanship and integrity and in going with the TV footage over the players opinion then it seems to me that the rules officials, perhaps unwittingly, brought the players integrity into question. That said, I'm not going to berate the rules officials who had a difficult job to do, which they did well and which they try to do to the best of their ability.
Final random thought; we often talk about bifurcation on this site in relation to professionals and equipment. It seems to me that we have a bifurcation taking place in terms of how the rules are applied. In matches below elite level it is for the players to make judgment calls and to apply the rules. It appears that no longer is the case at elite level.
Niall