I don't know. I think you could perhaps align incentives such that any bounty claimed via the government program is competitive, public, and companies are ranked by the number and severity of bounties. Then the company would have an incentive to run a bounty program where they had a chance of controlling the narrative a bit.
There are two entities that constantly and consistently stomp all over human rights and sovereignty - governments and corporations. It also seems that most people are comfortable with asking them to increase the amount of control they have over our collective affairs.