Why would an airport ever disallow landing approval?
The FBO or airport authority is collecting the fee. The tower doesn’t care about collections. I’m assuming a tower in your scenario. Non towered would mean they can’t deny you anything.
If the plane/pilot owes money, landing at the same airport is what they would hope for. Now you are on the ground and you get booted and can’t leave. No safety issue and they have possession of your airplane.