//...do they think we should simply have ignored the invasion and let the islanders be annexed?//
Yes I expect they do. But I don't.
Whether or not Argentina have a legitimate claim to the islands (and having read a lot about it, I suggest they do not) the invasion of them was not legitimate. I visited the Falklands before many people in the UK had ever heard of them. The people there are fiercely British and want no interference from Argentina whatsoever. Critics may say that's because we forcibly occupied them and installed a population there. History is unclear on that and I don't believe any Argentinians were expelled as a result of out activities. However, even if they were, we don't (or should not) settle things by invasion today.
Apart from being 8,000 miles further away, there is no difference between the need to protect the inhabitants of the Falkland Islands from foreign invasion and the need to similarly protect the Isle of Wight. The thing that sticks in many people's throats about the liberation exercise was that the decision to launch the exercise was taken by Mrs Thatcher, who also took some of the key decisions. It gives them a good reason to hate her even more. For me, it gave me yet another reason to admire her. The liberation was one of the most complex and difficult exercises undertaken by the UK military in recent times. Thanks to the defence policies of successive governments since, it could not be accomplished today and even if it could, I doubt any politician would sanction it for fear of upsetting a few people. No doubt a committee would have to be set up to conduct a review before any action could be taken. And by the time it reported (if it ever did) the islands would have been under entrenched occupation.