Blue, no, Animal Face off is NOT an accurate show.
[spoiler=long and rambling off-topic rant]They had an elephant versus a rhino once, and the elephant apparently won because of its 'superior intelligence.' So they had the right creature winning for the wrong reason (the elephant wins because it's BIGGER, duh). And then there was a crocodile and a shark, and the crocodile bit the shark at least three times, but the instant the shark bit the crocodile, the crocodile died. And the only reason the shark was able to bite the croc at all was because the croc needed to surface to breathe (which shouldn't even have been an issue, since those things can hold their breath for HOURS). And then there was a lion versus tiger episode where they spent about half the episode comparing stats like weight and strength and bite strength and the tiger won every single category but then they decided the lion should win because its mane protects its neck (which was the one variable they never tested).
So yeah, that show is full of BS. I don't know why I keep watching it.[/spoiler]
Anyway, as for the matchups:
I don't know why everyone keeps saying that the gorilla even stands a chance against the grizzly. Marco notwithstanding, gorillas don't really seem all THAT badass. All they have going for them is strength, which grizzlies have more of, plus grizzlies have teeth and claws too.
And I'm going to try and work out which animals would actually fight each other if this actually happened. Okay, go!
The lion would be most likely to attack either the rhino or the gorilla to start the fight, since those are its natural prey. It's probably going to go for the gorilla, since that's the easier target. LION WIN, GORILLA LOSS.
At this point the rhino would get pissed off and charge. It would probably go for a smell that it recognized as a dangerous one, which would be the lion. RHINO WIN, LION LOSS.
I'm assuming there's something in place to keep animals from attacking their own teammates? If not, the grizzly would probably attack the bull (which could be potentially seen as prey) or the lion (potential competition), and I think it would probably win either fight. Buuuut I'm going to assume it can't do that, so I'll say that it would be more likely to attack the gator, since it's smaller than the rhino. Unless they are in water, GRIZZLY WIN, GATOR LOSS.
At this point, the bull would charge the rhino. Or maybe the rhino would charge the bull. It doesn't really matter. They're about evenly matched, I think, but it doesn't even matter who wins the fight, because even if the rhino wins at this point, it will be very badly injured, and the grizzly would be able to able to finish it off. Alternately, if the rhino and grizzly duke it out, the rhino would be so badly injured from the run-in with the grizzly that the bull would be able to finish it off. GRIZZLY/BULL WIN, RHINO LOSS.
WIN FOR TEAM BULL/LION/GRIZZLY BEAR