I always, always, walk my boys on a leash. You just never know where or when trouble will be. My boys are like yours, ALWAYS very freindly, loving but I wouldn't know the day they just might not like some other dog, for what ever reason, and run over to fight. Or if there be a dog not on a leash who wants to start trouble I can have the upper hand controling my boys. Being on a leash will save you too, if there would be an altercation and your dogs are at fault and another dog is injured, you will just have to pay for Vet bills and not be fined for not having your dogs on a leash. In your case they lady with her dog was in the right. Her dog was on a leash, and she "could" do exactly what she said she would do to you. I believe it is just the safest way to go. Always leash.
At our dog park, two of my boys can run free but I still leash my Macs, at 10 lbs. he just has a "tude" sometimes. But he's working on it.....