Vanguard Australia is not owned by the fund members like it is in the US. Vanguard Investments Australia Ltd is a wholly owned subsidiary of The Vanguard Group, Inc. It's owned by the US company.
But the key point is that the funds are held in trusts the underlying assets are not owned by Vanguard and are usually held by a third-party custodian, making them unavailable to creditors in the event of default. So, even if Vanguard went belly-up, the bulk of the funds are safe. The other concern would be fraud, but I think I can rely on the Vanguard brand and Vanguard Australia's auditors to ensure that there's no funny business going on.
They better be safe, I have a couple of million in Vangaurd funds.