They are medical professionals, and thus held to the standard of only being allowed to call an ambulance. That was the whole point.
If your partner goes into cardiac arrest while you're driving, what are you going to do? Stop to apply CPR and while simultaneously calling 911? Start driving faster, running red lights, and hope you both survive the trip?
Or is your partner offering emergency services to the public in exchange for money? If so is your partner properly licensed and registered to provide those services? Is your partner insured to provide those services?
If you went to a licensed medical professional with your foot cut off, they're not allowed to call you a cab. They have to call an ambulance. You can tell them, to hell with your fancy EMT's and expensive rides, I'll just have my wife take me over to the ER to get this foot sewn back on, but they have to call an ambulance if you need transport. This is a liability and safety issue. It's also a kickback issue.
TL;dr- No, it shouldn't, and nobody wants to make that illegal.
A person with a severe impact might not have much external signs or pain, but could be bleeding internally. That would present a problem in the backseat of an uber on the highway.
Without stabilization, a broken bone can cut or puncture any number of blood vessels or organs (for a rib).
There's a reason we use medical transport after injuries -- you don't really know what might follow.
If the cost is the concern, using cheap transport isn't the answer. Either socialize the care or force workplaces to pay the EMT fees for workplace injuries. Sending someone in a cab is just not acceptable if a doctor deems medical transport necessary.
Now, all of this hinges on the particulars and accuracy of the description of the situation, which I can't really judge from the outside. But if otherwise independent medical professionals are being urged to reduce ambulance use in order to save face for the factory, that's a real problem. I'm inclined to believe the ousted clinicians and former employees, though.