I think the main question is, why was she told they could x-ray there, and then changed their tune when they found she had private insurance? What did those who did not have private insurance pay if anything?
The facility may not have a contract or be a provider with “private” insurance companies which means their claims would be denied, and they’d end up billing you the full cost of service (think arm and leg and first born).
If a government insurance...whatever the allowable rate is for medicare or medicaid (or whatever the individual state programs are for low-income families with children).
No insurance...whatever they want to charge as long as it is not less than what Medicare pays.
Regarding the radiology portion...typically the facility has a facility charge and a Radiologist charge, and then, if the Radiology group is not employed directly by the hospital or facility (most are not), then the Radiologist is billing separately for reading the xrays, but do not charge for the actual taking of the xrays. Dr.s most often do not take the films, the tech takes the films and then the Radiologist reads them.