It is a tough call. As a landlord I have played it both ways. I do have provisions in my leases that discuss different scenarios. For the most part I have told the tenant that if it is not identified at the time of their pre occupancy inspection then I will not cover it. If the property has a pre-existing condition, for instance, alot of homes have water ants that can be problematic on a seasonal basis, I do tell them that up front and that they need to be aware of it and deal with it.
I also apply what you said, hey if it is a good tenant and goodwill is kept by ponying up a few hundred to deal with the problem professionally I take care of it or maybe offer to split it or something like that.