My opinion is that to fix systemic unfairnesses ('the impartial referee') transfer of wealth is okay and to use those money to healthcare is just good use of resources if it goes to the target group. Bad luck is not an example of systemic unfairness. More difficult question is whether transfer of wealth is okay just to support naturally more unfortunate groups. I believe that is good, reasonable and beneficial policy but how to argue that everybody would be obliged to do this is a more difficult question. I'll return to it maybe later. Best I can now say is that currently democracy grants legitimacy for it, but this is bit shady as anything deriving legitimacy from democracy is circular as democracy is in effect legitimized by democracy...
On a side note... What amount/level/quality of information do you think the "the impartial referee" has? There seems to be room for debate in this area.