Mate of mine is military, apparently the tactical police crews cross train with the SAS, Commando Regiment and Navy Clearance Divers; and often have members of them on loan to them.
This. Make no mistake, these guys that make up the states tactical police units are ******* good. They may not be suited to traipsing through the deserts of Iraq and Afghanistan on LRRP missions like the SAS-R, but they are most definitely suited to handling urban hostage situations. Like you say, they often train with, and participate with the military in things such as NATEX, and in addition to what you've said in regards to members being on loan to these teams, it is not uncommon for the permanent members of these units to be former Army SAS-R or Commando operators. These people aren't just police officers taking a break from writing out speeding tickets wearing body armour and carrying assault rifles.
If shit really does hit the fan, and the situation becomes something deemed too sophisticated for the police to handle, then TAG East (made up of 2CDO soldiers) and the Australian Special Operations Command centre (SOCOM) is based in Sydney anyway.