As to whether or not he's just being overprotective, I would think that it depends on the age of the children. If they are teenagers, then that's ridiculous. If they are toddlers or elementary school age, then perhaps he's justified. Regardless, they are his children and it's his decision to make. Right or wrong - his decision.
I'm sorry that this issue has come up in your family. Maybe he'll change his mind. Maybe he could walk with his children once or twice and see how it goes. Maybe if you or another adult walk with them.
Its sad, but I don't think you will win an argument over it. Parents can be overprotective, and bottom line is he doesn't trust grandpa to be alone with his kids. Perhaps as he learns more about dementia his attitude will soften, if not then you will be better off to try to plan group activities and try not to make a big deal of it.
I'm sorry that this issue has come up in your family. Maybe he'll change his mind. Maybe he could walk with his children once or twice and see how it goes. Maybe if you or another adult walk with them.