Using Tom's answer as a starting place the wiki answer could be changed as follows:
Q. How can two people on opposite sides of the earth in Australia and South America both see the same South Pole Stars simultaneously?
A. The stars in the night sky are only visible simultaneously in these locations during a few months of the year. In those conditions it is questioned whether it is the case that the observers actually see the same stars simultaneously.
I'd suggest that the question should focus on the actual singular pole star, Sigma Octantis, and not 'stars', in order to avoid a tedious sidebar debate about what time and in what place the constellations like the southern cross can actually be seen. They may well be visible in those two continents at the same time, but if we focus on Sigma Octantis we don't need to worry about that, as it remains perfectly fixed in the sky and is therefore always visible south of the equator as long as darkness and clear skies permit it. If anybody is challenging this, that would be an extraordinary claim, as it would go against every single star map ever produced, and overturn centuries of successful celestial navigation. To that end some kind of proof would be needed, and not just vague statements like 'it is questioned'.
To that end, it's not clear why 'it is questioned'. It's the southern pole star - it's always there, due south, at the observer's latitude elevated above the horizon. It can be hard to see as it's quite dim, but that has nothing to do with 'only a few months of the year' - it's just quite a dim star, so you ideally need a dark sky and a telescope / binos to see it.
Moreover, whilst the focus on different continents is interesting, as it's so extreme, the problem it is highlighting is present for observers separated by only a relatively short distance in longitude, looking at the same star. On the FET monopole map, if they are both facing south (ie with their backs to North), then they will be looking in slightly different directions at the same object, which makes no sense at all.