Welcome to Beyond Blue. Private hospitals and insurance is a tricky field. My doctor wanted me to have a procedure and gave me a referral to a specialist, who has performed this procedure in the past. However, on this occasion I could not go to their (nearby) facility, which I went to the first time, because, since my previous procedure, the contract between the doctor's practice and my insurer had not been renewed. However the same doctor and insurance provider provided the service and the medical cover at another hospital. I hope that makes sense. So I could have the procedure in one place but not another. Don't ask why as I have no idea.
If you are looking for private hospital insurance you need to know which hospital you will be admitted to. Some psychiatrists have admission 'rights' to a hospital. These hospitals have, in effect, a bulk billing arrangement with some private medical insurance providers.
If you are seeing a psychiatrist it's best to ask him/her which hospital they are affiliated with and which insurance providers have partnership arrangements with the hospital. You also need to consider the waiting period the insurer mandates for some services. You may find you have to wait two/six/twelve months before you can access these benefits. At a guess I imagine the cheaper the insurance costs, the longer you will need to wait. But then I am no expert on this.
Surely your psychiatrist can send you to a public hospital if you are in need of this. I know public hospitals do not have the frills of private hospitals, but should offer the same level of service. I know there are all sorts of stories and experiences in public hospitals and I don't want to start a war about the pros and cons of different hospitals. The bottom line is, if you need to be in hospital it's better to go to public hospital than no hospital at all.
I really hope that helps you and I would love to hear from you again.