Yes do explain why private insurance paying into the public system if they are not in some way consuming services that would otherwise be available for use by the public!
What does the public system do with the monies received? Does it go into a black hole?
It seems reasonable to conclude that the private insurers are part funding the public system through these payments. It is not the fault of private insurers if the public system is wasteful with these monies.
And if private insurance companies didn't exist, all those people would still be consuming the same services and the public system wouldn't get one single red cent. Not a one.
The people with private insurance are still the PUBLIC. They pay taxes and private insurance premiums. They are funding their own treatments through private insurance and the treatment of everybody else through their taxes. They are not skipping the queue, they are using a queue that they created through their own funding to be diagnosed earlier, instead of adding to the 18 month or 24 month waiting list the public system has - and which they would be ON if they didn't have private insurance.
If your diagnoses reveals you need elective surgery, then you join the elective treatment queue you funded through your premiums. You place no strain on the public system.
Once you are diagnosed with something serious e.g. cancer, there is not much difference in treatment times between public and private - but early diagnosis can save your life for sure.
And in an emergency situation, e.g. heart attack, most people with private insurance are still going to end up in the public system.
So we all have a stake in the public system whether we want to or not.