Dog Leash Confusion

I'm hoping someone reading this can explain it back to me. I have had a situation today that just isn't calculating, so I'm reaching out for help.

First, there are some points of clarification. I live in the City of Denver, the County of Arapahoe and the State of Colorado which require your dog, unless in a designated area (e.g. a dog park) to be on a leash. It's called a Leash Law.

Okay, so with that in mind I also want to clarify that my dogs, Maddie and Kodiak, while sweet and innocent most of the time, are extremely protective of our apartment and surrounding areas. These two dogs are well behaved towards friends and strangers alike everywhere but our apartment complex. Around our apartment complex they feel the need to bark and sometimes growl at most people and every dog. It's something we're working on, but with limited success.

Finally, the story that I need help understanding. This morning I take the two pups outside for a little walk to take care of their business. We're only out and about for a short while before a small Terrier-like dog approaches without a leash. I think to myself, well that sucks but it happens. While my dogs go ballistic, I try to keep a distance between this dog and my insane and out of control, barking and growling, pulling and leaping pets. The dog keeps about 4 feet between itself and them, but then comes another dog, a chocolate chihuahua who isn't as interested in keeping away from Maddie and Kodiak. With one are extended holding the leashes of Kodiak and Maddie, I'm trying to use the other arm to keep these two other dogs away from mine. A woman casually strolls up, apologizes, picks up the two loose dogs (neither is wearing a leash that I can see) and walks away.

Okay, folks, that was my daily freebie. I understand dogs get loose. I understand people bend the rules about the leashes. It drives me absolutely nuts, but I'm not going to get myself labeled and the "cranky dog lady" in the neighborhood over it.

Four hours pass. The dogs and I are again outside for their benefit. I'm not 100 yards from my door when the same small Terrier-like dog is running for Kodiak and Maddie, who are again going out of their mind. This time the owner is kind enough to jog over, and she again apologizes. I respond with "that's why there are leash laws." Her rebuttal, "I know. She just always runs away. She always does this." And, her dog is now running away from her with the lady in pursuit. Again, I see no leash on this dog.

Here's where my question lies. Does a leash not tether the dog and person together, so unless the dog is significantly larger than you, the person can prevent the dog from getting away from the owner? Orrr, is there a new leash available that is invisible? I'm fairly tech savvy; I'd even say geeky. I'd think I'd have heard of it somewhere, but maybe I missed something. If you've seen a web page about this invisible leash, please link to it in the comments; I'd love to invest in some for Kodiak and Maddie.

This woman and her dogs are starting to really get on my nerves! And, while I am seeking some clarification, I also wanted to vent about this inept neighbor of mine. Thank you for your thoughts, support and willingness to read this pathetic and frustrating story.