I do think it's possible that Doc could have become associated with the legend of the lone dinosaur and could, perhaps, even be the new lone dinosaur. It may be possible that he's actually a relative of the original lone dinosaur (whoever his name may be), perhaps a son or, more likely, a grandson. And he learned everything he knew from the original lone dinosaur. And the original lone dinosaur may not have been the hero the tale says he is, but perhaps just an exceptionally good sharptooth fighter. Doc may be the same way. Nothing special about him; just good at fighting sharpteeth, likely due to him being a loner.
My guess is what happened is the event didn't even take place in the Great Valley, and that Doc's grandfather may have done something amazing involving sharpteeth (perhaps fight off a lot of big strong ones by himself) and dinosaurs who witnessed this with their own eyes may have started telling tales about him, spreading further and further away across the lands, and during each retelling, more and more things were changed, perhaps even how long ago it took place. The Great Valley may have become the location for the event maybe due to its legendary status in the first movie, and perhaps because of Saurus Rock.
I'm not sure if the lone dinosaur actually looked like how he did in the flashback; that was an interpretation and Doc just happened to fit that interpretation.