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Good article with the most details here:

In role reversal, president rescues Secret Service agent

http://www.washingtontimes.com/national/20041120-113709-8651r.htm

"The Secret Service source, who spoke on the condition of anonymity, said the president's security detail and that the Chileans had argued about security procedures all day and that he wasn't surprised to see last night's skirmish unfold.

The Chileans, he said, were determined to take charge of security, but the president of the United States is the only world leader who takes his bodyguards with him wherever he goes. Normally, foreign countries defer to that demand. The Chilean security detail resisted, the source said, and was determined to take a stand at the dinner.
"That's what the argument this afternoon was about," he said. "I saw this coming."

Chilean security knew that the Secret Service always accompanies the president and knows how to identify them by the pins on their lapels, the source said, but blocked them anyway. "