Bernese Mountain Dogs are like that, good natured to the max, perfect family dogs - forget about Cujo! Almost no hunting instinct either. The dog seems to be genuinely baffled at the squirrel's fruitless exploits. And the squirrel wouldn't be doing this if it wasn't totally at ease with the Bernese which it obviously doesn't qualify as a "potential predator".
I knew a couple who had one. A giant of a dog, but totally tranquil. Children could sit on it and ride it like a pony, it didn't mind. Nice boomy bark too, not that it would bark often.
