In other words, this can be seen as part of the free market incentivizing people and companies to find and patch exploits, or for programmers to just write safer code in general.
If an exploit is found, company A can play it for what it's worth, either accusing B of negligent behaviour, sloppy coding, defunct bug award program, etc., or exploiting the bug (via anonymously hired help) for a while, possibly in such a way that company B's customers notice the issue before company B does.
If an exploit is not found company A can still accuse company B of negligent behaviour if company B hasn't matched $X in their bug awards.
If company B has done everything right company A can pull the offer, and try to convince a reporter that this indicates an exploit was found and is being used without anyone at company B noticing. Dumber stories certainly have surfaced, and the damage could be significant.
you are right it's a human problem, and the problem is lack of respect for eachother. won't be fixed by any software patches for sure =]