Tom Cooper asked:

I understand your points and the reasoning behind it. My question is only:
why would the crew of the RF-4E in question then explain such a story?

Short answer...it would appear that since all Atolls missed, the
efficacy of photo-flash carts as IRCM was proven, at least
anecdotally. But wait...

What is missing from the story, are significant details like, time of
day (chased into the sun?), altitude of the fight, cloud cover (bright
white puffy ones)...even in the 80's the AIM-9 Papa was decoyed by
bright clouds.

After all, they said they used these cartriges to decoy the missiles, and
evaded four R-3/R-13s fired by the MiG in question, and also the Soviet
pilot rammed them in desperation.

Okay, here's a skeptical guess, merely throwing it out. What if the
MiG pilot was hosing off missiles from Max range in an clever attempt
to make the Phantom pilot turn, allowing the MiG to get closer (maybe
for a gun kill, not trusting the Atolls). BS? As the guy in the front
seat of the Phantom you would rely upon the WSO to tell you the MiG
fired a missile and which direction to break (assumes I can't see him,
i.e. he's in my vulnerable cone)

OK, the Atolls were not that problematic to evade, but an
RF-4E at supersonic speed is also not that maneuvreable either.

Indeed a big ass turn circle, which would give credence to the Max
range Atoll shot. Call me a skeptical asshole for thinking there is no
way in hell a Phantom is going to cruise Supersonic in Mil Power.

So from my perspective the supersonic RF-4 must be in Burner/Reheat/AB
and just think how much heat (IR energy) is thrown off by the exhaust
and the nozzles versus a few photo-flash carts. Based upon the TAWC
lectures and videos, I think it is unlikely photo-flash carts worked
as IR decoys under these circumstances.

As an aside, the mantra for using flares as IRCM included "ya gotta be
out of burner, and ya gotta maneuver the jet." So, here' what I'd toss
out. You've got an RF-4 going supersonic in Max AB, the WSO calls the
Atoll shots and tells the pilot to Break L/R, forcing the pilot to
Idle, Speedbrakes, and put 7.33 Gs on (and oh yeah watch out for Mach
Tuck as you slow down). Now the jet is subsonic and the fight stays
that way until they get speared by the MiG guy...AND perhaps the
mid-air was accidental.

Or you got this RF-4 going supersonic in Max AB and the pilot is smart
enough to try and keep the MiG(s) at the edge of the vulnerable cone
(out near the wingtip in terms of relative position seen from the FCP)
and out of Atoll parameters. These check-turns and extensions alter
direction, Left/Right in an attempt to keep going in the right
direction...Iran.

Tom this truly is an interesting story with so many missing variables
to ponder.

Do you have any idea what kind of cartriges were used at earlier times?

The reason that jumps out at me was the common belief that photo-flash
carts worked. There was no test data to support that belief, but what
the heck...photo-flash produce lots of light (energy) so they probably
will work as a decoy. I find absolutley nothing wrong with the logic
of that thinking (considering the infancy of IRCM).

Juvat