Not true at all, in countries with dual systems(public healthcare and private one) the private care usually acts as a shortcut to get things done quickly.

Often it's useful to get things going in private care and if you are not rich you can continue on the public system. The idea is that once you know which specialist you need to see, the waiting lists are shorter and you will be triaged depending on you situation. If that specialist happens to have long waitlist, you can choose to get private care and maybe get the actually expensive surgery in public hospital.