The 'knotted by dog story' is quite mysterious without further details. It might be a humorous account of a dog's clumsy behavior that resulted in a knot. For example, the dog could have been running around a tree with a long ribbon in its mouth and ended up getting itself all knotted up like a pretzel. Or it could be about a dog interfering with a human's work by creating knots in a ball of yarn or a fishing line that was left unattended.
Well, if it's called 'knotted by dog story', perhaps it's a story where a dog's actions led to a knot being formed. Maybe the dog was playing with a rope and accidentally knotted it up while chasing its tail or something. It could also be about a dog getting tangled in something knotted, like a net or some wires in an old shed where it wandered into.