I make no comment on the veracity of anything, as I'm not and never have been in the RAF. A quick Google ("RAF exercise Copper Flag Phantoms" were the keywords) brings this up from Hansard:
Copper Flag Exercises
HC Deb 22 January 1988 vol 125 c902W
902W Dr. Thomas To ask the Secretary of State for Defence if he will list Royal Air Force participation in Copper Flag exercises in the United States since 1977, giving the number and type of aircraft involved and dates of the exercise on each occasion.
§ Mr. Freeman The Royal Air Force has participated once in a Copper Flag exercise, which took place from 14 to 25 July 1986. Eight Phantom aircraft were involved.
Hope this helps.
LTL