I have been in the position of asking an aircraft with a problem, on behalf of the aerodrome authority, if he would consider going elsewhere. As we were his base he politely declined! It wasn't mentioned again.
beamer, in the circumstances you describe I doubt AAIB would want to attend before the aircraft was moved. In the last wheels-up I was involved in the permission to move aircraft came very quickly. Of course, how soon it is moved depends on the kit the airport have to do the job.
Of course, a quick call to D&D, who are the Executive Authority for all aircraft emergencies, may resolve any dispute.
This always amuses me. What dispute do you mean?