Yup, granny should have had control of the dog. On the other hand, it always bothers me that for anyone with a gun (LEO or not), the gun seems to be their first choice for dog encounters. I've chased away big dogs, little dogs, and even multiple coyotes, with just raised arms, yelling and making myself look menacing.
Not that there aren't certain situations and crazed dogs where a gun will be needed, but IMO, far too many people use a gun when other means will keep the dog from even getting close enough to justify shooting it. Meter readers and delivery drivers seem to generally get this. Cops, not so much.