Let me see. two wrongs here: An F-104 was not a carrier launched aircraft. An F-104 never carries nuclear weapons. Having flown and controlled them I know.
As another poster noted, this appears to be a typo and should have read F-4.
On the other hand, the F-104 was nuclear capable, here is a picture of the ordinance it was designed to carry:
http://www.wpafb.af.mil/museum/arm/arm13.htm "The Mk-28 "hydrogen" bomb, although first produced in 1958, is still an active item. It was designed to be carried by various fighter and bomber aircraft (F-100, F-104, F-105, B-47, B-52, and B-66)"
The important point again is that the planes were turned back not as part of a c-o-n-spiracy, but because they thought initially the attackers could be Soviets and they didn't want to start a war.