As a cyclist and also a dog owner I can see both sides to this.
Dogs need exercise unrestricted by leads, and for many the paths and parks near where they live are the only traffic-free places they can do this. Don't forget that the very paths that have now been labelled 'cycle routes' have often been used by walkers for generations. Cycle paths are generally 'shared use', and that means you have to expect to encounter walkers, children and dogs on them. Personally I slow down to a speed where I will injure neither myself nor the dog if it suddenly runs in front of me, much as I also do when I can see small children ahead of me. If I am wanting to avoid this I just use the roads instead. I use a Sustrans path daily to cycle with my dogs, and they are off lead. Because I ride with them they know not to walk in front of bikes.
As a general rule an off-lead dog is a safer prospect than a dog on an extending lead. That woman's crash is unfortunate and sad, although probably very rare. The only true solution would be to segregate pedestrians and cyclists completely. Roads did a pretty good job of this didn't they?