Yes, i know Fuchs was the man who did the actual crossing but In the OP I stayed Hillary "lead" an expedition to cross Antarctica. This gives the claim much credibility.
Additionally, there are many others listed who have crossed the continent and plenty of wiki links with further info.
Even, as you imply, Hillary's expedition didn't "cross" the continent then please extrapolate the miles required to journey from.Shackelton Base to Scott Base on your Flat Earth. How many miles would that journey have been?