You know, that's a darn good question. Dogs are in the same family as wolves (Canidae) but they look up more than they look down, but I would think that this is purely a result of domestication and looking up at people more, while wolves tend to keep their heads down to smell this and that - to track a scent of their prey.
No, I think as far as saying that "wolves have stiff necks" would be just as you say: a fplk tale. Because wolves keep their heads down to use their excellent orfactory system, while dogs look up to their masters because of their domestication. They no longer have to search for food: their owner/master feed them.