Ken,
I think your comments have been clear-headed and correct.
This situation should never have resulted in President Bush actually WADING INTO THE FRAY.
The SS agents should have a contingency plan that mirrors what you suggested: a clear, loud 'call' to the President and other SS agents that something unusual was afoot _to immediately alert them_. Their job would then be to completely close ranks around the President and, with just a split second to decide, determine if he should be thrown to the ground to be physically protected on-the-spot or hustled out of there as quickly as possible.
Kinda hard to do it they are outside, and he is inside. The Chilean TV report said that the Chilean agents thought the US agents were supposed to go in via a side door.
The video showed an AWACS as part of the security. That is not a good sign. Either they were worried about rogue elements in the Chilean Air Force, which doesn't seem likely. More likely they were worried about Jihadies hijacking planes and flying them into the meeting place. The formal dinner was canceled because the Secret Service insisted on all guests going through metal detectors. The Chileans said no to that, so there was just a small dinner with the Presidents of the US and Chile and their wives. (and some really tense security types on both sides one must imagine).