I always thought King Arthur were renowned for demanding tight specifications.
Hamelman shows in his book [2nd edition, pp.496] that the AP flour has a Falling Number of 281 seconds. The figure you cite here Chris is too low.
Anything less than 250 in the UK and the wheat would not be accepted by the larger millers to be used for bread flour. So you have 3 premium US brands here, lauded frequently on TFL, all of which would not make the grade in the UK.
Thanks for posting
Falling numbers are usually done at the flour mill. Testing of flour days, weeks, or months after milling could result in different numbers. Flour could gain or loose moisture over time affecting test results. No?
KAAP - can't say anything - I don't like it and I don't use it, but, yes, looks kind of low, since it's supposed to be in 230-290 range.
Gold Medal AP - GM specs for AP flour say 225-275, so within norm
Gold Medal Bread - specs say 240-280, low, but within norm
The other three results are meaningless, since store brands may (and likely are) sourced from different suppliers in different regions, although considering the fact that we have pretty much just three millers it's a bit surpising that there were no 100% matches. Although 365 is, of course, organic and therefore likely unmalted.