As others have said, his “hard cap” seems based more on what his own internal limits are (which are largely dictated by bad deals he’s already given out to middling players) rather than what the market actually will pay.
I think the NFL player agents are onto him. I picture Beane using one of those kidnapper voice disguisers to call agents and ask about the price of high-profile players, then quickly hanging up when they tell it to him. They recognize the hard breathing as Beane and it leaks out that the Bills are “in on” a certain player - they leverage that “interest” to drum up the market. But he’s not “in on” jack squat. He’s Guntekest 2.0.
Beane is your midwestern father-in-law. He loves to ask how much something costs, then give a low whistle and pride himself for not paying it.