Edit: I think I understand now....you are saying that the hash wont get propegated so unless the inputs are unique to me anyone can steal it....that sux :-)
Right, there is a subtle variant of Sybil attack here. Cathy is racing Bob to propagate their work certificates. Even if we told the story with 2 users acting as single peer nodes (not Sybil) on acoustic couple or home broadband Cathy basically still has a 50/50 shot at stealing any given work solution that she sees. At that point it would likely just come down to network routing topology.
With even a small out-resourcing (obv my story was over the top, by today's standards) Cathy could pretty much trivially ruin Bob's day the vast majority of the time.