A lot of zoos do produce koalas that will put up with handling and gentle petting; it's a good way to draw the tourists, especially the Japanese trade, which is a big earner here. But it's not their natural behaviour, and I wouldn't like to pick up even the tamest of them without a trained handler around to make sure it didn't get excited.

Also, being nocturnal, they're presumably quieter in the daytime, when most of the handling happens, than at 4 am when the theft took place.