Except under very strict circumstances, not charging everyone (including insurance companies) exactly the same amount for everything according to a practice fee schedule is illegal under the US healthcare system. Just because the insurance company doesn't actually pay the full amount (contract law gets mixed in here), it doesn't mean that a self pay patient gets to have free services. One reason medical costs are so high is because doctors are generally paid the lesser of the service charge amount on their fee schedule or the insurance company contractually allowed amount. Simple game theory dictates their prices be as high as possible.
Self pay patients can be charged less if a standard sliding fee schedule is created by the practice. This is to make sure that discounts are applied uniformly across all self pay patients against some criteria (e.g. 10% discount for families at 400% of the federal poverty level). I'm sure there are other ways too, but they must be applied consistently.
In the highly unlikely event the doctor's office is prosecuted for failing to charge her for a splint, I'm sure they could plausibly call it a billing error. Note that they didn't charge her less for the splint (which only cost them a few dollars), they simply took it off the bill.
I'd love to see the DA actually try to prosecute the doctor for this. It would make a great reelection platform: "I prosecuted doctors for failing to charge uninsured patients $300 for a $6 splint."
Self pay patients can be charged less if a standard sliding fee schedule is created by the practice. This is to make sure that discounts are applied uniformly across all self pay patients against some criteria (e.g. 10% discount for families at 400% of the federal poverty level). I'm sure there are other ways too, but they must be applied consistently.