Can eye drops intended for humans be used on pets (Read details)

My dog has bad allergies, and they act up in autumn. After a few trips to the vet, he advised us to get some regular allergy eyedrops (intended for humans, he suggested Clear Eyes or Visine)... and to use them on my dog just as I would use them myself.

However, my neighbor told me this morning that her cat had an irritated eye, and when she suggested using Visine (not on my suggestion, she thought of it herself) her husband panicked and told her not to. He said that he read online that it should never be done, and that is is very dangerous.

I Googled, and everything I’m reading says not to use human eyedrops for cats or dogs.

So… is the internet wrong, or is my vet an idiot?