Here's what you wrote (emphasis added):
A private medical provider charges whatever it charges. That's not extraordinary, but that's not the only claim you made. I'm asking for evidence of the particular claim you made, bolded above. Which private hospital is claiming a better cure success rate, for what major illness, and better than what alternative providers and therapies?
My apology as I mistook your query pertaining to 'extraordinary claims'.
The 'claims' word is in inverted commas, meaning doctors/surgeons will usually 'hint' but not directly giving 'guarantees' (usually 'options' will be given, then it is up to the patients to believe such 'claims' are true or not.).
Going for a second or third opinion for cancer treatments are not uncommon among patients and so different oncologist may have different approaches to treat the same illness. So, the said 'claims'.
