Rule 1: You probably shouldn't approach a stranger's dog. Well, ok, that's not exactly true. But you should never simply approach a stranger's dog without asking - from a distance - if it's ok. Some people don't want their dogs to interact with people they come across on the street. Some dogs look well-behaved but when they get around a human that is not their owner, they freak out. Even the most well-behaved dog is still an animal that acts on instinct and could flip out and attack if scared. Keep that in mind.
Rule 2: If you must approach a stranger's dog and the owner gives you permission, you shouldn't simply start petting it. Some dogs are picky about where they like to be touched.
Fortunately for people, Parker is a pushover and likes pats. Unfortunately for people, Parker does not like it when other dogs approach while he's on-leash. And yet stupid people let their dogs pull them towards us while yelling "Can he say hi?" No, he may not say hi, unless you want to pay both vet bills.
So pat Parker, but be careful of strange dogs you meet on the street.