RealUlli :
get told, "you can't land, we're full", things get interesting
This is where listening to the conversation would help determine who said what or misunderstood who. Airport full means gates and parking positions are full . an Airport decision .Nothing to do with ATC. That does not mean ATC can't land aircraft , they just won't be able to gets services. Happens relatively often , especially with massive diversions , due weather, blocked runway , terrorism , etc... Google Teneriffe 1977 or Halifax 9/11 if you want to see photos of examples. Safety first.