As someone who is terrified of dogs I get really anxious when I see a dog off the leash or on a very very long leash. I know a lot of owners are responsible and would make sure the dog doesn't run at me or jump around me. But I have also had plenty of experience of owners just standing by while their dog rushes up to me barking and leaping around the place. Reassurances that 'he won't hurt you. He's just being friendly' etc are absolutely no use in that situation. As a result, I really would prefer if dogs were kept on a leash in public places and especially if there is a sign requesting this.
Okay, that woman's reaction was over the top. But, as someone has already said, she may have had a few bad experiences from inconsiderate and downright stupid dogowners.