As Mr. Guffey's citation of the LA shooters suggests, heat travels. It always goes from a warmer area to a cooler one, losing temperature as it spreads. You can think of it as the temperature becoming diluted by the lower temperature in fresh material as it spreads. It doesn't have to spread far in most cases to drop below the annealing temperature.
For flame annealing, any visible red is too hot. The Draper point, at which a glow just barely becomes visible, is 977°F (525°C), so about 300F higher than is generally considered adequate for flame annealing. A true blackbody radiator theoretically just becoming visible at about 800°F (427°C), but cases are not true blackbodies (zero reflectivity), so the Draper point is probably a better guess. Hotter than necessary in either case.
Where this all gets sketchy is in timing. Brass crystal structure change takes time to change. At higher temperature, stress relief happens faster. At 570°F, brass is fully stress-relieved in an hour. At 700°F it's done in seconds. So if you get it red hot for just a fraction of a second, that should be OK, too, I just don't know what that fraction is. I do know that everyone I know who did flame annealing to a dull red glow in reduced lighting said they did it every three or four reloadings, otherwise splits would commence. Proper annealing should let you get the same 10 to 20 reloads that a new case fresh from the factory will usually give you if it isn't abused, so their brass was definitely weakened.
Stress relief (partial annealing) is all you need to eliminate work hardening caused by boundary dislocation so that it starts over. You will not fail to remove it completely if you don't anneal dead soft. Full annealing grows grain size and reduces tensile strength as the graph for a one-hour heat below shows, even if its time frame is different. Extra softening beyond the stress relief range just makes brass weaker. Brass hardness IS time and temperature dependent, as the fellows selling the AMP unit have proven by hardness testing and having to adjust their time and temperature controls to get the same hardness and every time.