I guess it depends on how much prior knowledge someone has of such problems. The correct explanation isn't "nobody noticed", it's "people noticed but could not/would not do anything about it". But how much you know about these problems will depend where you get your news from. If you never read right wing sources, you aren't exposed to stories about benefits/grants fraud as places like the Guardian or CNN just don't cover it, so all this will appear fantastical and absurd. If you're used to such stories then it all seems plausible and normal.
These types of things usually have some aspects in common. One is that front line workers, when asked in a safe environment, will give enormous estimates for how much of their payout is fraudulent. The people who are in denial about it are usually the people at the top, not the bottom. They don't ask, nobody tells, they don't want to know because they'll be held accountable for it and they fundamentally, ideologically, do not care about waste or inefficiency, viewing it as preferable to even one innocent person not getting their money.
I can't find it now but Musk has alleged similar things; he got private estimates from civil servants that 50% of the payouts from their department were probably fraud of some kind (it might not have been SS, I don't remember), and that the staff in charge of blocking payments at the Treasury were told to never do so. This kind of thing is what you'd expect. Often the front line civil servants are frustrated by this situation, as it's their taxes being wasted too. It's the people at the top who cover it up.