Actually, when he won races they played the national anthem, so I'd say Webber was representing his country.If players represented their country when playing in ATP/WTA tournaments then the Davis Cup and women's equivalent wouldn't be required would they.
A more correct explanation would be to say they are a type of ambassador for their country.
Mark Webber was not representing Australia.
Are you going to claim that cricketers who go to the Indian premier league are representing Australia as well?
How about boxers?
Agree that tennis players are representing themselves though.