It's worse than that, because there's adverse selection. The hospitals that make errors in the client's favor or that don't make errors at all are more likely to go out of business than the ones that make errors in their own favor. So guess which ones are still around when you need a hospital.

In other words, just because the errors are accidental, it doesn't mean they happen at random.

(This argument applies to any shady business practice that "looks" like an accident, for example dark patterns on websites, or having great customer service for taking your money but terrible customer service for refunding it.)

When the same agency is the one influencing, if not directly creating and enforcing, the process, my sympathy tends asymptotically to zero. Especially when said processes are largely driven by a motivation for profit, if not merely to exist as a middleman.