I can advise that, in the 2014/15 financial year, the Ministry received 12,530 fraud allegations from the public, staff and other agencies. Of those, 11,592 allegations were received from the public.
[...]
[T]he Fraud Investigation Unit completed a total of 5,342 fraud investigations and 927 successful fraud prosecutions in the 2014/15 financial year. There were also 1,619 overpayments worth over $51.7 million established during the 2014/15 financial year.
Overpayments aren't fraud, and most aren't detected as the result of public allegations (most are WINZ fucking up, which means someone getting a different sum from that which they are entitled to). There's also caveats around investigations and prosecutions not necessarily occurring in the same financial year as allegations. Still, the 2014/15 figures aren't out of line with their publicly released figures for past years, so we can get a ballpark solution. MSD seems to have taken "successful prosecution" as a proxy for "substantiated", so if we take them at their word, it suggests that 92.6% of all allegations of benefit fraud are false. And even if you buy into their "overpayments are fraud" line, then that means that 87% are false. Looking at investigations, over 80% of them don't result in successful prosecution. Which really makes you wonder if we're getting value-for-money from the Fraud Investigation Unit. Because on these statistics, it looks like they're mostly just spinning their wheels on pointless and intrusive snooping into innocent people.