Based on news stories I’ve seen occasionally, that’s exactly how [del]fraud[/del] over-billing is caught in the Canadian process.
Since there’s only one payer, and it’s all computerised, the Medicare officials find auditing very easy: «Computer! Give us all the bills filed in Town X for ear-wax cleaning in 2019!»
Je he computer spits out the info, and Dr Jones is off the charts for ear-wax cleaning. No other doctor in Town X has such a high rate.
So the bean-counters say «Computer! Give us all the bills filed by all Doctors in the Province for ear-wax cleaning!»
And Dr Jones is again off the charts.
So Dr Jones will get a visit from the auditors. Maybe it turns out that Dr Jones has invented a new marvellous technique for ear-wax cleaning, and is getting tonnes of referrals from other doctors, of patients with stubborn ear-wax blockages.
Or maybe Dr Jones is cheating the system.
Either way, the auditors for a single-payer system have a strong advantage over auditors in a private insurance system.
And that drives down rates of fraud (not Bryan Eckers´s theory about nice Canadians - sorry, Bryan. 
)
Criminologists have long been telling us that one of the best factors driving down criminal behaviour isn’t the severity of the punishment, but the chance of getting caught. If single-payer gives auditors better tools for catching fraudsters, then that drives down fraudulent behaviour.