The difference is that private insurers have an actual incentive against this happening but when the scheme is state-funded you have to rely on the people's sense of duty which we know is not particularly strong in many cases.
https://www.propublica.org/article/we-asked-prosecutors-if-h...
Investigations are a cost-center. Government can staff investigators; private insurers just factor the fraud into next year's premium hike.
> To put that record in context, take a look at the state’s Medicaid program, which covers about 13 million low-income people. During fiscal 2017 and 2018, the program’s fraud unit filed criminal charges against 321 fraudulent medical providers. It garnered 65 civil settlements and judgments and recovered more than $93 million, according to the state attorney general’s office.
> A rigorous search for civil lawsuits filed by private health insurers over fraud in California turned up just one case in 2017 and 2018. Experts said insurers rarely sue over fraud because of the high cost of litigation.
> I tracked down a dozen or so investigators who once worked for insurers, and they all said the same thing: Insurers don’t police fraud as much as they could because it hurts the bottom line.