Sounds to me like you ran into a "C-R-A-Z-Y" person. I don't know. This is a tough one. Since you do know that your dog can be dog aggressive, you should probably never have her off lead, since a dog can run up to her very quickly before you may even have time to call her back. But from what you describe of the other lady, she's a piece of work. And a very rude individual to boot! In the future should you encounter another situation like this (it doesn't have to be dog related), be polite and explain yourself (as you attempted to do so) but you DO NOT have to offer any credentials or personal details. She is NOT the police and you owe her NO details other than your sincere apology. If she wants to call the police, tell her, "go ahead". Offer to lend her your cell phone. I find that 99.9 percent of rude bullies decline when their bluff is called - especially when she was equally wrong!