Hardly anybody is going to actually try to keep a patient sick, but there are many other ways to get the same result.
Does this patient have good insurance? Run lots of tests. All the tests. Do expensive procedures that might help regardless of their cost benefit ratio. Spending a quarter of a million dollars for something that has a 2% better result than an alternative that costs $20 is perfect, because the incremental improvement is real. It's just not worth a quarter of a million bucks. But the patient doesn't care about that when it's the insurance paying.