The 'counter' to the Privacy Act is the Freedom of Information Act that makes allowances for the release of government-collected information that pertains to us personally. It's under this act that we can request & receive information on ourselves as well as deceased relations if a death certificate and proof of your relationship is provided. And I do believe this is where the 20 year time limit comes into play (your relative must have died 20+ years ago).
But in the case of Funeral Homes not only can they cite the Privacy Act they're also private companies who have the right to keep the information they collected private indefinitely. They own it, so they decide. Keep in mind that a funeral home record can hold more than just information about the deceased - it sometimes contains names & addresses of living relations and other sensitive information that living relations may not want released (even to another relation!)
Not all is lost though! Some Funeral Homes are happy to provide some information. It never hurts to call or write and ask what they would be willing to release (a funeral directors certificate of death?) and what documentation you would have to provide.
For more information on the Privacy & Freedom of Information Acts see the Information & Privacy Commissioner