UK and Argentina both claim the Falkland Islands - how can we know the truth of these claims?

Nearly three decades after the Falklands War, tensions between the UK and Argentina have resurfaced. The UK insists the Falkland Islands are rightfully the UK's. The Argentine government maintains the islands, which it calls Las Malvinas, belong to it. But what are the details of each side's legal, historical and geographical claims for ownership? This is a good example of knowledge claim, knowledge counterclaims, knowledge issues (how can we know the truth about who has a rightful claim to the islands?), ways of knowing (patriotic emotion versus reason, language as a source of knowledge or propaganda). The Areas of Knowledge would include History and Ethics (in international relations and the use of force by both sides in the war there in the 1980s). Examine this BBC page and see if the BBC manages to overcome any British bias to give a fair and balanced report of both sides of the question.
Is this a fair report? If yes, then it's a good example of reason triumphing over emotion, what do you think?
http://www.bbc.co.uk/news/magazine-17045169