Trads do not have the power to buy a place on the list directly. You're talking one powerful company versus another and the need on both sides to try to appear honest.
They do buy front-of-bookstore placement, but that does not guarantee bestsellerdom. Jackie Susann and her husband did some manipulating decades ago by sending out people to buy up lots of copies of her book at stores they suspected reported sales to the NYTimes list. But it's still pretty much a secret from where the Times aggregates the sales to compile its rankings.
Oprah recommending your book is still extremely significant, and Reese is also influential. The "everybody is reading it and I want to be like everyone else" phenomenon seems to be what creates bestsellers. But in a fractured media world, I don't know that these pockets of everybody add up the same way they used to.
As we all know, if you join the "right" box set, through various manipulations you can get on the USAToday bestseller list. Then you can put the label on all your own books. Does anybody reading and buying books really believe in that list anymore?