I suspect that regardless of the mode of transport, bonafides should be requested and provided to remove any doubt of credentials. If the episode of care occurred on the ground, then it is highly likely that those details would be requested/required from the practitioner by a police service (within Australia). The same could occur/has occurred on board at the request of cabin crew, or at the end of a journey by the AFP, or a similar agency if travelling internationally.
And I've never been required to prove my credentials if I've been a first responder. I've even rung up the hospital where the patient was transferred to follow up on care and all I've ever had to say is "this is Dr Artemis and I'm the specialist at xyz and I was wondering if..." Maybe we're too trusting.
But I think it's pretty apparent when people know what they are doing in these sort of serious accidents. Thank god for the emergency services - they absolutely know what they are doing and I am so grateful to hand the patient over for extrication etc etc. I think these non-medical types do a brilliant job getting people out of the most terrible messes... Must be so traumatic to do it day in, day out!