Though I am no expert on the subject, we did have an owner once claim that he had rising damp – in his first floor bedroom. A search of the internet provided information that rising damp is normally found something like 30cms above ground floor (or close to this figure anyway).
Not knowing your complex or its construction, if there is a slab construction in these townhouses, and there is damp above this slab area in the townhouse, then there could be a water/drainage problem under the slab. And I am pretty sure that any problem from under the slab is strata/OC. The owner is responsible from the top of the slab. Though your complex sounds like it has many different types of construction in it.
I have been told previously by our SM that our OC has an obligation to pay for the investigation of the origin of a problem to determine whether it is an OC or owner responsibility.