Nasty scenario! That's one reason I use airless tires.
But, while I understand the measurer's dilemma, one shouldn't schedule a measurement with no time available for problems. To help others avoid the issue, they should have patch equipment, and a plan for a flat situation. Set out a calibration-check course nearby (calibrate wherever, then set out two pieces of duct tape 1500 clicks apart. This way, you can verify no loss of air after your rides, and in this case, he could have done a modified calibration after fixing the flat. Yes, it requires getting back to the course, but again, must plan for problems.), and have some type of plan for transport back to that area in the event of a flat.
I know you can't always have a good backup plan. But, this does happen, and others have dealt with it.
I say go back on your own dime and complete the job. Not an attractive option, but it is better than hanging the race director out to dry. We contract to perform a service, and we need to deliver.