I can confirm this, having flown through airports in both places. I flew into Ushuaia from Buenos Aires and out of Punta Arenas, taking a bus between the two (since Chile and Argentina apparently don't get along all that well).

Speaking of which! The website also says "the team will link up with a British Antarctic Survey transport plane". The British and people in Ushuaia (and Argentina generally, although feelings seem to run a bit higher in Ushuaia) also don't get along terribly well. So, this may well be the closest a British team is able to get commercially and link up with a British flight to Antarctica.

Fun fact: the area around Ushuaia (Tierra del Fuego) has a beaver infestation problem, thanks to enterprising souls importing beavers there from Canada.