It's the WiFi and not the devices. I would guess it's hard to duplicate those issues without having 65,000 plus other devices going at one time.
If they are using regular enterprise grade WiFi, they are morons. Their application isn't anything like that. Their use case is probably closer to that of the military, but at least in the NFL, they have a fixed setup with no mobility requirements.
Noise is a huge, huge issue in crowded venues and that's if no one is trying to be a smartass and deliberately jamming the signal. I'm not entirely unfamiliar with trying to keep a network up and running in a hostile environment and the NFL desperately needs to apply even the most common of sense. First of all, they should be using hard lines way more than they appear to be. The sideline area should then be covered with directional transmitters to provide a focused area with high signal to noise. It's obvious that they are not doing this at the moment (all the visible antennas are clearly omnidirectional).
Considering their unique requirements (and $400 million Microsoft sponsorship with custom hardware), they should probably opt for a different frequency range than what is commonly used -- at least as a backup. They don't actually require a whole lot of bandwidth, but bandwidth is exactly what pretty much all enterprise equipment targets. Lowering the bandwidth allows you to operate in noisier environments with the same transmit power.