There are some COE built campgrounds that are run by contractors. The 'concessionaire' contract does not usually require that the honor of the Senior Pass Discount.
Usually such campgrounds are not marketed as COE Campgrounds and are not reservable on recreation.gov
If you have a question about any specific campground, go to recreation.gov and reserve a spot.
Just choose a date and campsite and work through the process to the checkout point That will give you an exact listing of charges and discounts. Cancel before paying for the site.
Some of us are old enough to remember some campgrounds that we now find are no longer run by the COE.
One of my favorites is a popular now city run park in the Dallas area. Another is a state park in Arkansas.