Is it a promise to reject any block contains a different transaction with the same inputs? That might leave the miner off the real chain forever
It would really be an insurance that if the chain confirmed a block containing a transaction spending the same inputs in a different way then the miner would pay the outputs himself instead.
With a sufficiently descriptive scripting language, issuance and enforcement of the insurance could be "automatic".
And if this works out, it pretty much solves the tragedy of the commons scenario for transaction fees. People with interest in not having their transactions double spent could buy such form of insurance.
The question that stays in the air is whether the risk of suffering a double-spend is high enough to motivate people to buy such insurances. But I guess that the answer to that is that, if the risk is not the high, maybe there's not so much need for mining power either. Safer is not always better, you have to take the costs into account.