"...How can Abbott explain something he didn't authorise and wasn't in charge at the time?..Zonetrader"
Abbott is the current PM, and the responsibility falls to the current PM, (part and parcel of the job).
All Abbott needs to do is to give a public apology (as the current PM of Australia) on behalf of Australia, and give assurances that the same thing won't happen under his watch.
Indonesia knows spying goes on, but because it is now public, Indonesia just needs the apology and assurances to save face.
