Of course they'll never be perfect, but the official estimate would need to be off by at least an order of magnitude for it to matter vs. the harm done by government.

If it's that far off, there's at least half a dozen editors of major UK papers that'd be rubbing their hands in glee at the opportunity to further demonize benefits claimants by exposing more benefits cheats and/or by exposing flaws in the reporting. That this isn't happening despite both commercial and ideological gain to be had in doing it if they could, is to me a strong indication that the numbers aren't that far off.

If the sample is randomly chosen shouldn't it have proportionally as much fraud as the overall system?

I think the suggestion is that they'd be unable to detect it in many cases. And that's a fair point - of course some portion of fraudulent claimants will succeed in hiding it. I just don't think it's likely to be a sufficient portion to make much difference.