Having kept dogs for over forty years I (and SWMBO) are still appalled by the number of people who will not keep Fido on a leash in public places. A dog does not think (regardless of what certain blinkered owners may say), it acts instinctively and will wonder round at will if allowed too. I believe but stand to be corrected by our "legal eagles" that a dog involved in an accident is deemed out of control if it is not on a close leash and the dog owner or the person in charge of it is responsible for it's behavior. As for speed; well we live and learn and some times make mistakes and most of us learn when we can and can not put the foot down.
The way I control dogs on a shared path is in stark contrast with the way majority of people do, and they see nothing wrong with it because it's not
dangerous at that moment, but not being aware whose on the path around you, or where your dog is
dangerous because it's out of the owner's control, and in my opinion the dog is then out of control and that doesn't have to mean it's acting aggressively at all.
There's very few people that I pass that are actively aware of what's going on around them, just like we're expected to as cyclists/motorists when in control of anything that requires 'control', shared path, shared responsibility. Not everybody shares the same view, so it comes down to experience, it's usually pretty easy to spot a dog owner, and if there's any large groups or people who have stopped to have a chat, it's usually safe to assume there's a dog running around somewhere.