Yes, it's a true story.
We were at medium level, VMC between layers, conducting surface surveillance in support of the main TF somewhere south of ASI. While it wasn't quite a QRA style flying alongside and taking photos/waving copies of Playboy lookover the 707 (coming from the south) made a turn about 1000 feet above us, descended slightly and approached from about the 3 o'clock before making a leisurely turn in front of us and slowly disappearing from view. Probably a mile or two away at CPA.
Although we broadcast the details on HF and UHF (the HF was heard back at ASI and by forward elements of the TF further south), nothing was heard on board the main part of the TF about 50 miles away where the Harriers were (or so we were briefed) holding cockpit readiness with the aim of splashing the B707. Comms with the RN were ever thus!
Yes, it's said that it was that encounter (I believe there was another, though perhaps not so close) that led to the MR2 fleet being fitted with Sidewinder.