Based on this book http://www.amazon.com/gp/product/1591145198 and much else I've learned on the subject, the above story is wrong in most every particular. Specifically:

"Maneuverability" is not the end all and be all of air combat, else we wouldn't have, for example won the air war in the Pacific in WWII. Energy from position (being above the enemy, or diving to gain speed) and from energy–maneuverability theory (thrust to weight ratio plus drag), see also the linked https://en.wikipedia.org/wiki/Aircraft_specific_energy when combined with proper tactics can beat pure maneuverability, especially if the latter is gained at the cost of things like pilot armor and self-sealing gas tanks (Japanese Navy planes were optimized first for range, and then for maneuverability, and were crippled by nonavailability of better engines). The classic tactic for attack is called boom and zoom; per this gaming wiki entry (http://wiki.warthunder.com/index.php?title=Boom_and_Zoom): "Boom and Zoom (also known as BnZ) is the name of a play style that aims to take advantage of a high energy state to bounce the enemy, avoiding any prolonged fighting in order to conserve speed and/or altitude."

Once you factor that in, the only bad match of the war was the F-105 and the Mig-21. The F-105 was designed and used for ground attack, so if Migs were allowed to get at the bomb laden F-105s the results were frequently not pretty.

That happened a lot for a bunch of reasons, e.g.
because the Air Force's F-4s were still using a WWII era flying formation, which reduced their fighting power to 1/4 of the Navy's. F-4s were for a long time only equipped with missiles, which was very bad because the Air Force's models of them were particularly unreliable in the field, the fact that almost all the planes in the air were ours meant visual recognition was almost always mandatory, so the intended scheme for Sparrows couldn't be used. Their pilots were in a 1 year rotation schedule, replacements were poorly trained, and didn't have the floor in competence the Navy required for carrier landings.

By comparison, the Navy's Sidewinders were better (both it and the Sparrow were Navy missiles, ditto the F-4, the Air Force really didn't like this and that's supposed to be one of the reasons they kept with their WWII formation, couldn't admit the Navy was also right about that), they started out with guns + Sidewinder pure dogfighter in the F-8 Crusader, they trained for air combat (e.g. the famous Top Gun school).

By comparison the North Vietnamese tended to follow Soviet doctrine, which depended on precise control from the ground (which they had, since this combat fought over North Vietnam), the Mig-21 in particular was iffy for dog fighting due to terrible visibility from the cockpit (some NVAF pilots in fact preferred earlier Mig models), and they used two general tactics: for offense, hit and run, trying to get bomb carrying planes, for causing them to drop their bombs so they could maneuver was a win, and a defensive one where they flew in a wheel which was very dangerous to attack.

To finish, for air combat, getting in an tight dogfighting OODA loop represents a failure of some sort in the first place, Energy-Maneuverability Theory was an implicit thing going back to at least WWII, and unlike the Air Force, given all the limitations in place the Navy did rather well, although it tended to burn out its pilots because they didn't have enough to rotate them, and the carrier landing requirement strictly limited getting replacements. And OODA loops don't matter for two very common and important types of "dogfights", where either the target never realizes it's under attack before being fatally wounded, or the attack forces it to abandon its mission and flee.