That's the issue. The broadcaster, CBS, NBC, etc. pays millions of dollars to broadcast that footage and it doesn't exist unless they - or someone - does and puts it on TV. So to just hook up a cable to your PC and directly repost it as either a video or gif and call it "fair use" doesn't fly. I don't like it, but I understand it. Local television affiliates have to get permission and even they're limited to how much of it they can show. The only ones with the freedom to do whatever seems to be the official team sites, which obviously makes sense.
Same thing with photos. If I take a photo from camp and post it here and someone comes across it via Google Images and posts it on their site, Twitter, Facebook, etc., they think it's fair use because "they got it from Google". Well, it wouldn't be on Google if I didn't put it on the internet for Google to put it there. And if I didn't say you can use it, especially if you're not at least giving us the decency of crediting the fact I took it, you can't. Go take your own stinking pictures and then you can use them