Looking at the problem academically, it boils down to whether a live sporting event can be copyrighted, and US courts have ruled that they can't be (unlike dance and music performances). The BTN broadcast of the event is itself copyrightable of course, and any re-broadcast or misuse would constitute infringement. But the True-Wrestling Guy's [TWG's] footage was his own, and his work thus enjoys its own copyright protection; his broadcast can't infringe on BTN's. So if BTN came after him with a copyright infringement claim (and I don't know about BTN's approach, but plenty other sports leagues/teams do misuse copyright law in this way) he would have a solid defense.
That said, I'm fairly certain that on the back of the ticket into BJC is some fine print restricting videotaping and subsequent broadcast, which is perfectly legitimate and common enough that most everyone uses the same boilerplate language. Whatever remedy BTN might seek against the TWG would need to involve BJC/PSU somehow and rely on the argument that TWG breached the terms of his ticket purchase. And there's also [I'm guessing with some degree of certainty] a contract between BTN and BJC/PSU guaranteeing BTN exclusive broadcast rights, which BTN could say that BJC/PSU violated by failing to enforce its own agreement with its ticket buyers.
But the law is far fuzzier with respect to remedies and violations of ticket buying public--usually the venue will just kick you out if they see you filming. Nearly happened to me recently in fact, seated in front row of a Susan Tedeschi and Derek Trucks show at the Beacon in NY; usher warned me repeatedly that I couldn't shoot using a "professional camera"... luckily that usher was replaced by a less strict usher and I wound up getting great shots. And there's nothing the band or the venue can really do about it now.
Bigger picture, though, is that IP law is prohibitively expensive to litigate, and leveraged rights-holders routinely, successfully bluff with little fear or blowback. But if BTN did go after TWG, TWG would prevail in a litigation where money was no object.
