Bretton Woods wasn't about military protection. It was about stabilizing the global economy and monetary system. It absolutely gave the US a ton of economic influence, but it didn't have anything to do with military protection. The Soviet Union even took part in the negotiations that turned into the Bretton Woods Agreement, although they chose not to sign the treaty.
The US' military hegemony came out of NATO, the Cold War, and the Marshall Plan.
That didn't happen when just 1 Senator went and didn't live stream his visit. If they really wanted to, they could have claimed he did something violent or something. There'd have been no way to prove otherwise. And he was able to get them to crack just by holding a press conference. The bad PR from 1 guy getting denied scared them so much that they let him meet Abrego Garcia.
So why do you think they'd do that if there was a large group and the entire thing was being live streamed?