I can't speak for Australia, but in general you definitely don't need to burn for increased cancer risk - a clear example of that is the fact that artificial UV tanning beds lead to significantly increased rates of cancer despite the fact that they're used in such a way that you tan without going far enough to burn.

Although we often think of burning as bad and tanning as good, tanning is nonetheless still actually a symptom of your skin being damaged by the sun - it's just a symptom that looks better than burned skin, to the point that many people think it looks nice enough to be worth the cancer risk (and/or don't understand the risk when they decide to tan).