If anyone's querying whether this really happens, my airfield took a diversion from Birmingham last year - a largeish piston cessna with a gear problem. Turns out he was inbound to BB and couldn't get three greens. After the pilot tried to rectify, but was unable to, BB told him to sod off because they didn't want their runway blocked.
TBH, since a controller cannot deny a landing clearance, I wonder about whoever held him and alerted management, rather than pressing the big red button and making him #1. I wonder how they would feel if the problem had become something much bigger while he was diverting.