It's been a while since I've sailed from San Juan, but I believe that embarkation takes place on deck 4 or 5 as it does in other locations.
Having been an EMT for 17 years, based on what was in the doctor's report, my guess is that people would be running away.
They do not embark at pier level, but on deck 4 or 5. As you said, the only people on the pier should have been workers.
Just to clarify, the doctor would have had access to the crew gangway several of which would have come directly off the pier onto deck 1. Passengers would use these to embark and disembark at ports of call during the cruise. Passengers embarking on that day in San Juan would do so on the elevated gangway from the cruise terminal building onto deck 5 as you noted JulieBEMT.