Maybe people were more trusting back then because scams weren't as common - but some cheques were still rubber, so you'd think some proof of liquidity would be required before such a massive purchase.
Especially as it was so long ago - an amount like that would buy several houses 30 years ago (average Australian house price was $184k - in places like Tassie, far less - I bought my first house for $70k around then).
There are people who win multiple times, I'm no statistician but I believe the odds are exactly the same each time no matter how many times you've won before - so while it appears strange, it's probably not.