This appears to be speculation repeated often enough that it has become fact. However, while there was one F8U-3, BuNo 146340, on flight status at Langley from June to October 1959 (they were stricken in November), this is almost certainly apocryphal.
It is true that two F8U-3s were ferried by Vought to NASA Langley in mid-1959, BuNo 146340 on 26 May and 146341 on 27 June. The former was assigned to sonic-boom research and the latter, relegated to being a hangar queen for spare parts. It is also true that F4H-1 prototypes were at Patuxent River during this time for brief periods (27 July-13 August and "October") for Naval Preliminary Evaluations, the former (Phase II with #6 for local carrier-suitability evaluations and the latter, Phase III with #3 for AFCS and inflight refueling evaluation). While it's possible that by happenstance (it's hard to imagine that it was planned, a good way to get grounded forever) an F4H and F8U-3 were in the same airspace at the same time and at least one pilot decided to briefly abandon his planned and important test flight to tangle as fighter pilots will, it's unlikely at the least.
Moreover, Donald Mallick was one of two NASA pilots assigned to the F8U-3 test program. He wrote a memoir that is available online, or at least used to be, for free:
It includes a candid and detailed account of his F8U-3 experience. Given that by the time he was writing it he almost certainly would not experience any reprisal (nor would the other pilot, who was killed while making a flight text evaluation of a Blackburn NA.39 Buccaneer in England in early October just before NASA F8U-3 flights were concluded), it is inconceivable that he wouldn't have mentioned an impromptu encounter with an F4H.
Nevertheless, it is very likely that if there was a dogfight between the Phantom II and the Super Crusader, the F8U-3 pilot would have won it.
