If I'm at the dog park, and a dog comes up to me and solicits attention, I will pet them. Norris will wander up to people and sniff them, and allow himself to be given a few pets, but he's no attention wh*re (except with me). I tend to be sitting on the bench in the corner because dogs have a habit of crashing into my legs while they play for some reason and my knees can't take too much of that.
It's hard not to touch a dog at the dog park, especially when you are sitting on a bench and they throw themselves at your face all HAII!! There was a 10 month old shepherdy type mix who threw himself at my face three times, and it wasn't until the third time that the owner yelled at her dog, and she didn't even apologize to me once! Yeah I'm at a dog park and some dogs aren't very mannerly and will jump up, but an apology from the owner is only polite.
As for picking up other people's dogs, I generally don't do that. Although once somebody brought two dogs into the park, and one of them was an elderly toy poodle who clearly didn't want to interact with the other dogs, and was very obviously asking to be picked up (almost climbing into your lap) and so several of us picked her up and cuddled her. The owner wasn't even paying attention to what this dog was doing, so I guess she was ok with us picking up her dog. We didn't have a small dog section then, but one was recently built. Small dog owners don't really use it though. A lady brought in a tiny schnauzer creature, must've been no more than 7lbs, and an american bulldog type sniffed the schnauzer (probably schnoodle actually) and suddenly flipped out barking and snarling and the owners grabbed the bulldog (who then redirected on an English Bulldog in the same family) and the schnoodle owner picked up her dog. Neither owner left the dog park. Norris and I left at that point.
The Bulldog shouldn't have been in the dog park. But I always worry about tiny dogs playing with 50lb+ dogs as well. I've seen dogs jump over each other, slam into each other and even do unintentional somersaults. What if a big dog landed on your 7lb dog and BROKE it?? Too big of risk IMO! I'm glad that Norris completely avoids little dogs, he thinks they are boring, lol.