The land you refer to is owned by Lonna St. Martin. And it's likely that she was the person you spoke with. She is a Tribal member. The land is not Tribal land, it's private, but it is owned by a Tribal member.
Back in the early 2000's, Lonna let anyone go across her land to access the lower part of the Wind River (e.g., the Bobber Hole), which is just upstream from where the Tribes set their hoop nets. However, the crowds got too big. That's what happens when 30,000 spring Chinook return to the Wind River as they did in 2001. So she posted the land, and locked the gate. She sold the keys to whoever she wanted. Not sure the price since I never got any. I just stopped going there. Some guys really like going upstream to some of the holes below the falls, as you mentioned.
However, I've fished the lower Wind River the last couple years. I just park up the hill, and walk down to the Bobber Hole. If you do that, you are not trespassing on private land. Just don't go upstream too far.
Not sure why Lonna no longer lets anglers up there, but the sheer number of anglers probably has alot to do with it. And, it's her land. My sense is that she would allow the Tribal folks to go up there, but not sure why they would. The hoop nets at the lower end will catch alot of fish without hiking up into the canyon, and then back down again, with fish.