I'm wondering though, was I an SS because my dog slipped out of its lead? Maybe I deserved their reaction?
You're not a SS, but neither are the couple whom your dog approached. They had absolutely no way of knowing your dog was friendly, and for all anybody knows, they and their dog have been attacked before, so they are frightened when strange dogs approach them unleashed. Their reaction was extreme, but not completely uncalled for. I think the swearing and screaming was over the top, however and they should have apologized for that.
Your dog should absolutely not have been able to slip out of his collar. Beagles have little heads and can easily get out of a regular collar, and I do think you should have known that. A harness would be better for a beagle. Lessons learned and all that.
Dogs should be able to slip their collars if they pull hard enough. This is to prevent them accidentally hanging themselves.
Firstly, thank you to everyone for the interesting replies. I do know that I was in the wrong for a) letting my dog slip her collar and b) chasing after her with the other dog in my hand.
The dog has never slipped her collar before. I don't know why it happened this time. No she does not need to be in a harness, they make her uncomfortable and difficult to control - she responds much better to a sharp tug around the neck (we've tried, she won't even walk with a harness on)
Maybe I was the SS for thinking the other people could remain in control of their animal and not try to seriously harm mine. She responded when I called stop but they kicked her, so of course she was going to get upset and anxious and not listen to me. When I was at puppy school, my instructor said that the best thing to do when a dog is running at you is to remain calm, control your own animal, use firm (not shouting) words and try to walk away. I have done this and even large dogs will just get bored and leave us alone. I understand the guy being scared, I would have been too, I was just really scared of him. He looked as though he might physically harm me if not for my friend. I have tightened Charlie's collar and changed my route.
I've since heard, from neighbours and other people I see on our regular walks, that this man will yell at anyone who even dares to walk on the same side of the road as him

I don't have any stories about one, thank goodness, but I think flash mobs are by definition special snowflakes.
I used to think flash mobs were very cool. That is, until I was confronted with one that blocked my way to uni so I couldn't get to class. People were standing around watching which made the crowd + flash mob take up so much space that the only option was for me to walk back the way I had come and around the long way - about 10 extra minutes. I was not happy.