While this may delay the process, ultimately I expect that the person who signed the rental agreement will be responsible as they have been unable to properly identify the person operating the vehicle at the time of the offense and hence they are still responsible for the vehicle's operation at that time.

A Stat Dec is a legal document and if two people each complete a Stat Dec stating the other was driving at the time, then one of them has made an incorrect statement and I expect each could be required to show why they believe their statement to be correct.

The Qld traffic infringement process is such that if the fine is not paid or a Stat Dec identifying the driver submitted within the defined time period, the matter goes to court. So then it is up to the magistrate to determine who is responsible for the infringement. And being a non-resident, attending court is unlikely to be a desirable outcome. So I suggest that if the two people cannot decide, then its going to rest with the person whose signature appears on the rental agreement unless they want the matter decided in court.