Caffeine is toxic to most animals. Milk chocolate has so little actual chocolate in it that there's virtually no caffeine, so that's why your vet tells you not to worry about the snickers bar. If you eat dark chocolate because you're not a troglodyte then you might have more to worry about

It's bad for their kidneys, it's not like they are going to keel over and die right away, but it's going to hurt then long term and shorten their life span.

I mean, you wouldn't let your dog smoke would you?

American "chocolate" is not real chocolate. But it's still bad for dogs.

I imagine, the problem comes in from there being wildly different sizes of both, dogs and chocolate.

I once heard a story, where a small dog had eaten chocolate, so the owner called the vet. And at first, the vet told them that it's probably fine, but wanted to know how much chocolate the dog ate.

And when they then told the vet, that the dog had eaten a full-size chocolate bar, suddenly it was treated like an emergency. As in, they had to bring the dog to the vet immediately, got treated before everyone else still waiting, and the dog was given a drug to make it puke out all the chocolate.

How is a snickers bar the example of chocolate you chose? It's like what, 10% chocolate at most? And milk chocolate at that.
No matter, it's not exaggerated because it's never been "if your dog has anything with cocoa in it it'll die immediately!!". Chocolate isn't good for them so just don't ever give it to them or leave some in a place they can get to.