As a dog owner and runner, maybe I can intervene with some idea of why dog owners say the things they say...
A dog is a pack animal. They're born with instincts to chase things, especially things which appear attractive or interesting - such as cats, other dogs (especially), cyclists, runners and even cars (in some mental dogs' cases).
The owner says "if you stop he won't run after you" because quite simply, the minute you stop, you become less attractive (you're not trying to get away) because obviously if you're trying to get away then you must be worth chasing!!
This is not compatible with the runner's ethos of "not wanting to stop" and breaking their stride/pace etc. However, the dog isn't capable of reason or thought (even though some owners swear they are) and so if you keep running by him, he'll keep chasing!!
As for the dog's who bite runners - that simply is a question of poor training and dog management. Dogs only bite those things they perceive as a threat. It seems to me that those pooches who aren't "socialised" early enough to respond to different aspects of their life - i.e. runners, cars, other dogs etc are likely to respond in an aggressive manner. In my opinion this is lazy dog ownership and if a dog bites you - you ought to ask the owner their name, address, details of pet insurance and pass the problem to the police. People who have dogs that bite in public can be ordered to make their dogs wear a muzzle when out, even if they do not come under the dangerous dogs sections of the law.
RoadRunner -- most dogs aren't required to be on a lead in a public park unless that park's byelaws specifically state that it is so. However, a dog owner is legally obliged to ensure that his or her dog is under control at all times. To me this means putting your dog on a lead when anyone he doesn't know comes by - or attracting their attention with treats and biscuits etc. If the dog isn't under control and you feel the dog poses a threat, you are entitled to report the dog owner to the police for this and they can be fined upto £2000!!
Hope this helps - so if a loose dog is chasing you, the best course of action and easiet (because of their stupid owners) is to just stop and wait for the owner to get hold of the dog whilst you carry on. Sorry, but you can educate dog owners until you're blue in the face but you'll always come across some prat who doesn't understand they have a responsibility to the public when out with their dog.