G'day Crosshair,
Very interesting point you raise about flying schools and renting of aeroplanes. They are probably under no legal obligation to check your ASIC but consider a scenario that occurred recently where an o'seas pilot was hired an aircraft without an ASIC and proceded into a security controlled airport. Ultimately it is up to PIC to ensure he has all appropriate licences and documents for the flight, however it could turn into a very expensive aircraft recovery job by the flying school concerned because they failed to exercise the slightest duty of care prior to hiring out the aircraft.
Maybe a fine, lots of paperwork and certainly your name flagged up on the database when you do apply for an ASIC. Operating without an ASIC is one of those "aviation security offences" which will automatically disqualify you. Give it a go and let us all know how you get on.