It doesn't look like they had kept out his entire detail. There are at least three people who look like secret service agents. Both men to the President's right have earpieces and one appears to have the same vest as the President is wearing under his suitcoat.
However, the dispute has taken their focus away from the President which is a critical problem.
My assessment is that (in that photo, MediaMole) those several standing immediately by the President as he approaches the fray are not USSS, but rather, Chilean protection service amd[protocol types. Further, if the USSS were standing next to him, I am sure they may have blocked the President from getting into the fray. He's walking over pretty much on his own here.