Earlier quoted context omitted.
That won't help you there. Germany's public healthcare system denies plenty of things too, and will only pay for treatment when you sue (or know someone who works there). Germany's private healthcare system on the other hand is usually better (I'm sure there are exceptions and some insurance company that sucks).
You can have good public healthcare without the need of the notion of 'claims'. The Scandinavian healthcare system is a good example ( https://en.wikipedia.org/wiki/Healthcare_in_Denmark ).
The one benefit (I guess) of universal coverage is that doctors already know the unapproved medicines won't get paid for, so they never try. So you avoid the whole issue of rejections. They just go with whatever the system says it will pay for.