Fact: Melaleuca Alternifolia grows in Australia.
"The native habitat of [Melaleuca] alternifolia is a small area of north-eastern New South Wales, Australia. However, [Melaleuca] alternifolia has been cultivated successfully in other parts of New South Wales, in other states of Australia such as Queensland and Western Australia and in other countries." http://www.attia.org.au/teatree_about_faq.php#009
They say that Melaleuca Alternifolia grows in other countries, but I am still doing more research on that.