I42 - theres no need for them to keep quiet, independence from the UK is not a frowned upon view in Falklands society, its a minority view, but an entrely acceptable one - the reason almost no one votes for it is that almost everyone on the believes that if they became independant, and the UK military left, they'd be Argentine citizens within the week.
if they trusted Argentina not to either invade, or coerce them into 'choosing' to become part of Argentina, or indeed trusted the rest of the World - the US primarily - to uphold their right to self determination as a small independant country, there would, in my view, probably be a 10% for independence (legal independance, rather that cultural/societal detachment from the UK) - but they don't trust Argentina a nanometer, nor the rest of the world, so for them the reality of independance doesn't really exist...