NHF – new heroes for Heroes V 3.1.

How can Necropolis buildings help an opponent?

Nope.
Necropolis captures a town, converts it.
The former owner (or any other player) captures it back, converts it back, and the buildings are restored.

The true state in this case is the one that existed before the spell was cast, and in each iteration, it's the previous state.

Ah, I see. Then it's a different matter. I thought the true state was what it would be if the spell hadn't been cast at all.