The BO already rented her arena to her boarders for all the riding they would do. To now rent it to the pro is renting it out again a second time for the same ride, same boarder and same hour. This is not like renting out a salon chair where the store owner has not been paid until she is paid once by the stylist.
If I were a boarder and asked to pay a ring fee for my lesson, I’d want the arena to myself. That would make sense, right? After all, I had already paid to ride in the arena with nothing special when I paid my board bill at the beginning of the month. So what extra am I getting now? And again, if the fee gets passed on to me, as it will because perhaps my pro would find a place I could haul to and not pay a fee, so she says “stay home and pay your BO’s fee or haul to me; your choice.”
You also didn’t address/don’t value what a traveling pro brings to a BO in the form of engaged, safe-riding boarders.
I do understand that fee charged to an “outside trainer” if there is an in-house trainer. After all, that pro would like to have a captive audience in her set of boarders who really don’t generate any profit.