The budgets are still separate. 

There is nobody who sits down for each patient and each appointment and says 'Hmmmm .... we can send a community nurse over to do this procedure, or we can send an ambulance to bring them to the hospital and do it there ... what's the difference in care and cost?'

There is nobody at the hospital who points out that sending a patient home without supplies doesn't actually save any money, because the supplies provided by the community nurse will come out of exactly the same budget. So patients get sent home without supplies, since then the cost comes out of a different budget.