Taylor understood the pilots carried out training flying and that was when the incident occurred.
The tourism operators had told him the jets were "flying low in our airspace", and were concerned enough about safety issues to ring him.
When he rang US personnel, they said they would talk to the air crews.
The RNZAF would also have "shown them where they could and couldn't go and do that sort of flying".
F-16s can reach speeds of nearly 2500km/h.
US Air Force F-16 pilot Richard Smeeding said before the show his jet would "let me pull minus-3 to 9.9 Gs, go twice the speed of sound, rage through the mountains at 100ft fully loaded for war and all the time flying like an extension of my body".
Fox Glacier helicopter pilots contacted yesterday declined to talk on the record.