Quotes from this federal webpage:
https://www.fs.usda.gov/visit/passes-permits/recreation-fees-passes
“Concessionaires may or may not honor his pass, according to the terms of their current permit.”
“Concessionaires may or may not honor the Interagency Annual Military Pass, according to the terms of their current permit.”
“Concessionaires may or may not honor this pass, according to the terms of their current permit.”
“Concessionaires may or may not honor this pass, according to the terms of their current permit.”
Looking back at my reservation.gov history, I have 9 previous federal campground reservations. 5 out of those 9 did not accept my American the Beautiful Pass. I have no way of telling which ones were privately managed but one can assume. I’ve stayed at several first come first serve federal sites and don’t recall any issues with those but I did stay in 2 places that were reservation only and reservations were managed on the concessioners website. These were Pisgah National Forest and the Badlands. At that time, 5 years ago, neither of them honored my American the Beautiful camping discount.
I have also passed on several federal campgrounds reservation specifically because the concessioner did not accept the discount.