I'm into minimalist shoes and barefoot generally, but there are some circumstances where proper shoes are the more suitable surface for most people.
The absolute worst surface for running in minimalist shoes is a canted slope (cambered to one side) with stones, such as a rocky field. If it's a muddy, soft surface then you won't do your body any harm even if you heel-strike, as the ground will absorb as much of the impact as your body.
I would seperate running for your enjoyment on trails from running therapeutically as your physio has advised. The latter can be done on firm, man-made surfaces over relatively short distances. He's right to suggest that running up hills will help teach good form.