The reason is simple and you kind of answered it already, the shop you’re using does partial pressure blending for any mixture aside from air, and banked EAN32. Partial pressure blending is when a tank is filled with hyperclean 100% oxygen then topped of with hyperclean air, basically if the tanks weren’t O2 cleaned, during the first step of this process the volitile 02 would react with the oils, and other contaminants, and basically eat your O-rings and tank away possibly to the point of combustion. Why both tanks? Who’s to say you won’t oneday want some other mix that has to be blended in both tanks? In Fla, and most other tourist spots, your tanks never come in contact with 100% O2 so no need to worry there.
Another reason is that it’s the shop’s pump and so it’s their rules about what gets hooked up to the pump.
Bottom line they’re looking out for you and them. Just do it. Just wait till you decide you may want to get into Tech diving and you have multiple regs that have to be O2 cleaned too. $$$$