This is going to be something of a sideways answer. I'm going to explain why it's possible to find a "yes" and a "no" to the question, and for them both to be justifiable, and both to be supported by good references!
There is no single unique calculation of total greenhouse gases emitted. One has to specify a particular boundary for the calculation; and the boundary one chooses, affects the answer. As your sources show: with one boundary, Australia will have the highest per-capita emissions; with another, it will not.
In particular there are three dimensions to the boundary that each make a big difference: the what, the where, and the when of emissions.
What: The first is which emissions one includes: just CO2, or the Kyoto basket, or all significant greenhouse gases. And how thorough one is in measuring emissions from land use, land use-changes and forestry (LULUCF), and of fugitive emissions from extraction, transmission and distribution systems, and flaring
Where: Whether one attributes fossil fuels emissions at the point of extraction (rare, but not unprecedented), or the point of combustion.
When: What time horizon one selects: and that's because the ratio of greenhouse gases, and in particular the ratio of methane to CO2, varies between countries; and the global warming potential of methane, relative to CO2, varies significantly, depending on whether one uses a 20-year horizon (56:1), 100 years (20:1), 500 years (6.5:1), or whatever.
Australia, as your own references indicate, is one of the highest per-capita emitters in the world. It's a major coal miner, so has high fugitive methane emissions. Given those relatively high methane emissions, there are at least three ways that changing the system boundary would also increase Australia's calculated per-capita greenhouse=gas emissions, and thus potentially push it up the rankings:
- counting methane as well as CO2, particularly if we include fugitive methane emissions from coal mining.
- attributing by extraction rather than combustion;
- using a shorter time horizon (NB this only works if methane is included in the calculation.)