No you can buy Bitcoin anonomously it is just rarer than the way you advised. From a site on Bitcoin buying in Australia is this:
"If you want to buy bitcoin in Australia, most exchanges will require you to verify your identity first. However, if you value your privacy, it is still possible to buy bitcoin anonymously.
The following are some of the available options:
- Using a peer-to-peer platform like LocalBitcoins to trade directly with a bitcoin seller
- Using a bitcoin ATM to anonymously deposit cash, have it converted to BTC and then transferred to your bitcoin wallet
- Buying bitcoin with a prepaid credit card or cash via a platform that doesn’t require ID
- Trading altcoins for bitcoin on an exchange that doesn’t require proof of ID"
My Newsagency is able to printout the Bitcoin “voucher” and I believe there are a few of them who do it.