At the time, the only direct flight out of Sao Paulo to South Africa was every other day; which was why all the teams except Peggy and Claire flew to Europe for connections to South Africa.
Peggy and Claire got done in by a weather delay into London, and security screenings (that Race was filmed just a few months after 9/11) which prevented them from making the connection that would have gotten them into Cape Town at about the same time as the other teams. The best they could get then was a flight 24 hours later.
Since then, the schedules changed, and when teams had to fly from South America to South Africa for TAR AS (I believe), they were able to get direct flights. The longest leg on record though, was the uber-leg in TAR 9, which had teams going from Patagonia in Argentina to Moscow to Germany on one leg.