In the wild, many parrot species will spread their wings wide and hang upside down to get water on the underside of their body. So yes, they do like to get wet all over!
Some of the rainforest birds spend almost all their time in the trees, and get their drinking water from sources like rainwater that's been trapped in a cupped leaf. But cockatiels are ground-feeding birds in an arid habitat, and they get a lot of their drinking water by wading into a pond. This link has some pictures of wild cockatiels drinking:
http://www.arkive.org/cockatiel/nymphic ... 36339.htmlThis might be the reason that some pet cockatiels prefer to bathe by wallowing in a bowl instead of a mist bath. In the wild they'd be wading into the water basically every day, but rain showers would be infrequent.
This link has several pictures of wild cockatiels drinking at a watering hole in Queensland:
https://www.flickr.com/photos/marj_k/86 ... otostream/