It really is a clusterf*ck.
My gf got sick on a flight. They did the whole nine yards and called for a doctor. At the end of the flights, it's SOP to get the paramedics. Since she was starting to feel better at the end, they said to wait in the back, and we'll let the pax deboard first. We all agreed to this, but the paramedics wanted her off first, so nobody on board was aware of this, so they made everyone wait til she got off first. It was a mess.
btw, in case you're ever in such a situation, if you want to just leave (which we did, since she was starting to feel better), be firm with the paramedics. They just waste your time by taking blood pressure, asking your weight, and other stupid stuff. When I pointed out that she'd vomited a lot, and asked for an IV, they didn't even have that. So don't waste your time with the airport paramedics. For the most part, they only have a wheelchair and can call you an ambulance.