Would I take someone flying on a local trip as a 'last wish' kind of thing? Definitely, if his doc agrees. Would I have undertaken the flight proposed to the OP? Definitely not.
Although I honestly have to agree I share the same feeling I wonder what the difference, and therefore the deciding factor, really is.
I don't think flight safety considerations would be different between the local jolly and the intended transportation flight. I assume that the OP and his aircraft would be quite capable of making the flight in one go, so no hassle with an intermediate refueling stop. In a further post Pace referred to an unpressurized twin at 10.000 feet so I assume an IR, and thus weather should not be a problem, and neither should be a fairly long overwater crossing to get a direct route.
Yes, with a longer flight duration the chances of the patient dying en-route increase too, but they increase linearly unless the sickness is somehow airpressure related. (Probably not a good idea to take a lung cancer patient to 10.000 feet...)
Or would it be lack of suitable alternates if something does go wrong? Or maybe some sort of legal issue, like immigration of a sick person, quarantine (MRSA like I mentioned) or the legal complexities of somebody dying en-route?
If a person dies on a local jolly, or on an international transportation flight, I guess the family is just as likely to sue (or not).
Note that I'm still assuming that the flight can be made without any medical staff in direct attendance. So we're not talking a medivac flight with all the bells and whistles, in which case I agree that even a local jolly is best left to the professionals.