On major UK airlines, both the crew and any medic who steps in to help are insured against any claims from the patient.
The BMA were complaining that there is no internationally, or even European, recognised standard for, or assessment of, the medical care that is offered on airlines, and (I think) that the minimum standards required are not sufficient. They were not saying that all (or even most) airlines do not do enough, just that there is no way of knowing what standard of care you can expect.
It's a reasonable point - but trust the BBC to drag DVT into it. I thought the BMA chap explained very clearly that DVT was not fully understood, and that it could affect people whatever the reason that they were sat still - train, bus or car jouneys, or sitting at a desk.