Well, as I stated above, it's simple math. Disregarding the heat factor, of course. Yes, 4351 psi is 299.99 bar. Always has been, always be. (I cannot speak to what some company from China claims it to be)
Also, Boyle's law has been around since the mid-1600s. Can't really argue with them maffs. And the math in your quoted post is as accurate as mine is, but we are talking about 4500 psi, or 310.26 bar, and THAT is what leads us to 97 cu ft as opposed to 88.
To be clear, a 9L/550 cu in tank filled to 4,070 PSI (280.6 bar) will hold 88 cu ft, whereas filling it to 4500 psi (310.3 bar) will result in an air volume of 97 cu ft.
(And that firman's rating... we need to just drop that from our vernacular, as it is useless, even for firemen; anyone should be able to deduce that a 110 lb female firefighter won't draw as much air as a 210 lb male firefighter. And BOTH of those will draw more air, thereby reducing the time a tank lasts, when they are stressed and exerting themselves.)
Thanks for pointing out that post!