The rules for distinguishing between alligators and crocodiles are not very helpful in most of the world, because in most of the world either (a) no crocodilians are present, (b) only crocodiles or only alligators are present, and you should not need to tell the difference between anything, or © whether or not it’s a croc or an alligator doesn’t matter, you still shouldn’t be anywhere near it. (also caiman and dwarf crocodiles confuse things a bit)
That being said, to the best of my knowledge, most of the rules are in fact true. The tooth thing, the head shape thing, etc. The important thing to remember is that alligators are stub-faced chubby bunnylizards, whereas crocodiles are snaggletooth goober-monsters.