This is kind of a weird area. I only have the US FAR/AIM in front of me, a lot of this is harmonized internationally by ICAO but I'm not sure how complete that

This is kind of a weird area. I only have the US FAR/AIM in front of me, a lot of this is harmonized internationally by ICAO but I'm not sure how complete that is in these more edge cases. But in general there is no procedure that allows a controller to "take command" of an airplane, however, there is a procedure (this is ICAO harmonized) for the military to instruct aircraft via emergency security control (ESCAT) or intercept. In the case of ESCAT the book doesn't say compliance is mandatory but rather expected, so presumably a PIC could refuse to comply under the normal safety of flight rules (a pilot is not obligated to obey any instruction that, in their judgment, puts the aircraft in danger). In the case of intercept compliance is mandatory, but intercept is also a very specific procedure which is not reported to have occurred here. At least from the reporting it sounds more like the fighter that was sent appeared as an escort, which is a distinct situation from intercept (and fairly normal in a bomb threat situation, in order to immediately report the what and where if a bomb does go off to speed SAR response). For the US rules see AIM 5-6-12 and up. It does not appear that any of these rules were invoked in this situation.