Without intentianlly causing offence to anyone who may be in govt housing, if you rent it to DoH then you have no control over the tennants that they put in the house.
If you rent it to anyone else you get to deicde based on their applications and have a better idea of the sort of tennant you are getting.
That's basically what I was going to say - through DOH you won't know who it is going to be renting.