Over the years, I've had one dog that would find and catch rattlesnakes. I didn't dare let him off leash because of this tendency. My current dog is a German sheppard mix that likes to chase things that run so I also always keep her on a leash. While hiking in Escalante a few years back a lizard ran across the trail right in front of us and the dog went after it like a flash, right over the edge of the 30 foot or so cliff. Luckily, I'm a big guy and was able to pull her back out of mid air onto the trail without the leash breaking her neck. Had the wife been on the other end of the leash they would have probably both gone over.
Myself, even the well behaved dogs I keep restrained as they're dogs, and sometimes act instinctively no matter how well trained.