Whilst it is easy to suggest the medical crew were having fun hedge hopping, I suspect there is and will never be a shred of evidence to support it.
Having managed systems both sides of the Atlantic I encounter medical crew raising issues of flying below limits even when not true but never encountered them supporting dodgy rides. Ie medical crew tend to be over conservative.
This accident most likely arose from pilot error, but in terms of general accident rates time and again I have noticed flight crew change their attitude to a flight if they know the medical basis is urgent. If you tell a pilot it is a sick child or a pregnant woman, let alone tagt the patient will die if they don't fly, it inevitable changes judgement. Get there iris.
The systems I have seen in the US seem to provide this information to the pilots. In the system I have run in the UK we don't tell the pilots the medical mission merely the route. I like to think we have lost a few more transfers but taken a few less risks.