This is definitely a thing, they do all kinds of things like counting things before and after the surgery to avoid it.
The flip side is "sorry, we didn't have enough surgeons available right now so we have to triage you", or, "sorry you can't afford the bill"
I'm sure in this particular situation the numbers benefit "don't leave surgery debris in the patient" but the more general point remains, there is some set of numbers (likely implausible) where it would flip the other way