You can influence the payment processing. And if the crypto would allow false payments, it’s value would immediately drop to zero. The more money you have invested, the higher your incentive to keep it’s value stable.
PoS validators have the power to propose new blocks and attest to the chain head. They cannot change the state transition function to allow false payments, just as BTC miners cannot use their block proposal power to mint arbitrary coin amounts.
PoS has a concept called "block finality", where once a block has been marked finalized it cannot be reorged without committing to getting slashed for 1/3 of total staked ether (several billion dollars). Blocks typically get finalized after 6 minutes. This is possible because you can explicitly check whether validators have voted (attested) for two separate blocks at the same chain height.
It is not obvious to me that an agent with higher investment should be allowed to notarize the payments. The system should generally work for the benefit of the users, not the HODLers, developers, miners, stakers or any other special interest group.
P.S. I think PoS is a major downgrade in decentralization. At that point, you might as well just use classical consensus: it's more secure as your relationships with notaries are explicitly established as opposed to choosing whoever happens to have the most coins.