Not that I think there’s much credence to this signal as you’ve stated it, but it does have overlap with what I try to convey to people when I ask them to leash their own dog: it’s for the safety of their dog as much as it is for mine. In other words, as I’ve tried to explain it, “even if your dog is perfectly well behaved, you have no idea if my dog or any other you may encounter is a danger to your dog.”
This has been universally unconvincing to those dog owners who walk their dogs off leash. They don’t—in my experience—actually care if it puts their dog at risk, any more than they care about putting anyone else at risk. Anecdata still, but my experience tells me that whether a dog is leashed or not is mostly an indicator of whether the dog’s human is more concerned with the dog’s safety, or with their own selfish convenience.
This is 1000% my experience. Even farmers with working herd dogs, who can completely trust their dogs because they work off-leash 10+ hours per day, still clip on a lead in public.
It's not because they don't trust their dog. It's because they don't trust OTHER people's dogs -- especially because a good 80-90% of people with off-leash dogs don't actually have control of their dogs. They just really like the aesthetic of an off-leash dog and, by golly, they're going to do it--even if they haven't put in the gruelling training it requires, and even if it means their dog is endangered by other dogs. They don't care or think about it because they don't actually have a deep bond with their dog and value it; it's an accessory.
This has been universally unconvincing to those dog owners who walk their dogs off leash. They don’t—in my experience—actually care if it puts their dog at risk, any more than they care about putting anyone else at risk. Anecdata still, but my experience tells me that whether a dog is leashed or not is mostly an indicator of whether the dog’s human is more concerned with the dog’s safety, or with their own selfish convenience.