Not impossible, it;s called transglutaminase:
I believe the FDA considers this safe. Someone here said they bought a steak from Walmart and it's texture when cooked was more like ham... well...
Having watched the video you linked and skimmed the blog, I have a couple of comments on the "meat glue" thing that might be a bit off topic for this or not:
1. Yeah, so? Maybe I just spend too much time in my kitchen, but I thought this stuff was common knowledge. I've been using it for several years to help stick together haddock and cod filets if I'm wrapping them around a seafood stuffing or similar. Helps the food hold a shape that's nice on the plate as well as bake evenly.
2. This enzyme is also part of something known as "molecular gastronomy" - people pay big bucks to eat in restaurants that use this stuff and lots of other "mad scientist" things in the kitchen to make unique and tasty dishes.
3. The enzyme itself, in foods, is just another protein along with all the others and harmless, so I'm not sure what the big deal was in the video about "this stuff is dangerous". I wouldn't snort it like cocaine or anything though.
4. The video did have a very valid point about bacterial concerns if you've got "glued together" steak cooked rare or similar as there can be lots of voids that don't heat completely and you could get a dose of something nasty that way.
5. Item four is why I agree that it most certainly should be labeled just like meat/fish is labeled for "previously frozen" or "wild caught" vs. "farm raised" and other such things. Still, the point of the video seemed to be that it was more a concern on the restaurant table due to their suppliers using this process than it was in the supermarket meat case.
It's always the fine balance between "just tell me what I'm eating" and "I'd rather not know how the tasty, tasty sausage is made".