It seems we are both right, based on how the system has evolved today:
https://bfgnet.de/c-and-i/tax-free-shopping.html
Note that goods under EUR2500 may be paid for directly. That is possibly where the Army/RAF systems had differed in the past, and I suspect (but can't remember) the threshold either wasn't there at all, or was much higher. I certainly bought cars and caravans from dealers (ie considerably more than EUR2500, but in DM at the time) using the system and never once did I pay the Army, it was always to the dealer.
The purchase may well have been officially in the name of the PRI or the unit, but I don't recall that. It was a green form, and needed to be validated with a unit stamp. Our admin office issued them, same as Benzinscheinen.
Larger retailers, eg. Kaufhof or Hortens would take the Abwicklungsschien without issue. Smaller ones sometimes had to be persuaded. Given the amount involved (15%), it was a simple decision to purchase elsewhere if the retailer wouldn't accept it, and find one that would.