Recently they don't, anyway. I mean, it's no massive secret, but I've just been having a glance through, and the extent to which it's true is truly remarkable.
Between 1989, when Australia became a team of note again, and the end of The Ashes 2006/07, the games involving them which were drawn with no interference from rain numbered 15. This out of 197.
Out of interest, these games are:
2005/06 vs SA at the WACA.
2004 vs SL at Cairns (and they were within 2 wickets of winning this)
2003/04 vs India at the SCG
2001/02 vs NZ at the WACA (and New Zealand should have won this and were only stopped by bad Umpiring)
1998/99 vs Pakistan at National Stadium Karachi
1998/99 vs Pakistan at Peshawar
1997/98 vs SA at Adelaide (and of course South Africa should have won this and were only stopped by bad Umpiring, the infamous Mark Waugh game)
1997/98 vs SA at the MCG
1994/95 vs Pakistan at Gaddafi Stadium Lahore
1994/95 vs Pakistan at Rawalpindi
1993/94 vs SA at Kingsmead Durban
1993/94 vs NZ at the WACA
1993 vs England at Trent Bridge
1992/93 vs WI at the SCG
1990/91 vs England at the SCG (and England should have won this, they allowed the last 4 batsmen to survive 200 balls to take Australia to safety )
1989/90 vs Pakistan at Adelaide
1989/90 vs SL at the 'Gabba
As you can see, the trend's even more astonishing since The Ashes 1998/99, when there are just 3 uninterfered (counting Ian Robinson in 2001/02 as interference) draws out of 98 games.
There's so much about Australia in recent times to marvel at, but this is one of the highest heights.