You're asking them to show proof of a null, which is tricky. For example, a landlord could tell their tenants to make the check out to their spouse, deposit rent checks into their account, then turn around to the government with their usual tenant bank account and say "They're stiffing me on rent!"
The government would still go after the tenant to potentially pay back the money that the gov fronted to the landlord (or a portion of it based on means testing). Then the tenant would have incentive to provide proof to the gov that those checks were written out. And the landlord then gets thrown into federal prison for government fraud.
They could catch you retroactively when you report the rental income. Of course you could simply not report the income and hope you don't get audited but at that point you're now also guilty of tax fraud with the intent to conceal your wire fraud, and tax fraud is the type of thing the IRS can sniff out even years after the fact. There will be no plausible deniability possible since the unreported income will correspond to the defrauded payments, it'll be an open and shut case.
We don't exactly prosecute for fraud very much in this country. Otherwise we would see a lot more business owners going to jail for immigration fraud, tax fraud, and wage theft.
The government doesn't have perfect information.