http://www5.austlii.edu.au/au/legis/cth/consol_act/ca2001172/s104...

http://www5.austlii.edu.au/au/legis/cth/consol_act/ca2001172/s1041e.html  - Corps Act s1041E.

Doesn't matter what medium that a statement is published, if it's false or misleading and it is likely to induce people to acquire or dispose of shares (a financial product), or to is likely to affect the price of a financial product traded in a financial market in Australia, then it's an offence.

So exactly what happened to Musk in the US is entirely possible for any Aus company directors who use twitter, or any other media, to disseminate information. Only difference is that in Aus, ASIC is not likely to do anything about it if they stay true to form