I don't think anyone is claiming "flame" heating isn't a valid way to anneal brass. The argument is whether you can control the brass temperature, from day-to-day, as well as you can with a salt bath.
First, there is no practical way to measure peak brass temperature with either method. The problem I see with flame heating is that the rate of heat transfer is highly dependent on the adjustment of the flame ... nozzle distance, flame length, angle of impingement and flame temperature. Time exposure can be well regulated with an automated system, but that's all. Since the flame temperature is well above the desired annealing temperature, all adjustments must be well controlled to produce a consistent output ... although eyeball adjustment may well get you close enough.
With salt bath heating, salt temperature can be easily controlled within a range of 5 °F, and immersion depth controlled very accurately. With a 10 second immersion time, brass temperature will be within a couple degrees of the salt ... every time, every day. Immersion times are controlled manually and are somewhat variable, but can easily be kept within 10%. So it comes down to which method you believe produces the most consistent brass ...