I feel people are responding a bit aggressively to this post... The OP is sharing a issue that many parronts feel is important.
Most people can agree that mammal saliva in general is bad for parrots. Parrots aren't mammals, and unlike us generally cannot handle gram negative bacteria(which includes salmonella) and run a risk of becoming very ill. But if they do come in contact with the saliva they won't instantly die, maybe their wasn't enough bacteria, or the bird has a particularly strong immune system. Birds are much healthier in today's day and age, with the improved diet many they have are given the best chance to have a stronger immune system.
Rosie has been in contact with dog saliva once or twice, and she has had food, or drink water, that had come in contact with my own saliva when I was new to parrots and didn't know any better. But just because everything was fine, doesn't mean something couldn't go wrong in the future.
It's understandable if birds come into contact with saliva unintentionally, but it's not something we, as parronts, should encourage. Why risk it bY allowing constant exposure. I'm not saying they shouldn't have contact with the other animals, it's just a good idea to try keeping our avian's from ingesting mammal saliva. Better safe than sorry.