Depending on the country that the diversion occurs to, the traveler may not have legal status to enter the country in their own right. The airline (as the delivering carrier) would have to stand guarantee to sponsor the person's entry, as well as any repatriation, medical and accomodation costs involved.

That is partly why airlines will usually prefer to return to originating station than divert to an en-route point in the case of a medical emergency (other factors also come into play obviously).