Yes, and a 737 has nowhere near the range to get from Edwards (Los Angeles area) to South Australia....hell, even 747's have been known to have to come to ground for fuel before they even get as far as Sydney...and southern Oz is another hour beyond.
Exactly - I see I wasn't the only one for whom this bit stuck out. The latest model 737, according to this page from Boeing, has a maximum range of 3383 statute miles. This handy air distance calculator (LAX to MEL, if you feel the need to try it yourself) tells me that the distance from Los Angeles to Melbourne is 7923 statute miles.
Not that mere facts are usually enough to trip up proponents of theories like this, of course...
I guess the questions would be, what were the dissimilarities between the aircraft they used and and the 737, and is it possible to bring them into line with a 737? Fuel capacity seems to be the problem. Could it have been solved without being obvious about it, or without witnesses?