The ESA isnt a governing authority here. The proper analogy would be two planes in uncontrolled airspace on course to come uncomfortably close. One asks the other to change course, and the other refuses. No FAA involved.
This sort of thing actually happens with some regularity. Airliners and other fancy planes carry TCAS systems which can detect other planes and tell the pilot to maneuver to avoid a collision. If the other plane has TCAS, the two units will coordinate to ensure they don’t both dodge the same way. TCAS can also detect planes that don’t have TCAS, which would be virtually all small planes, and in that instance the TCAS-equipped plane will maneuver to avoid on its own. Airliners routinely fly though airspace where not all traffic is under positive control by ATC. Sometimes they end up on a course that sets off TCAS. The airliner will then maneuver to avoid the collision while the light aircraft pilot remains blissfully unaware, unless they happen to see the airliner fly past.