I don't think that is true at all, it is very clear that identical procedures and materials cost less in other countries.
Yes, things cost more in the US, but the volume is also quite a lot higher.
If a scan is more likely to cause harm than to treat illness is it really being rationed, or do single payer systems have an easier time not providing harmful over-testing and over-treatment options?
The opposite is often said for the NHS in the UK - certainly a smaller buyer than the US aggregate, but maybe a larger player than any one of them?