The Falkland Islands number 778 and MOST of them are uninhabited.
Two can play at being bloody pedantic.

Yes, but (generally) when referring to "The Falkland Islands" one is referring to the islands as a group, and the group is inhabited.

The British Isles are also inhabited, although some of the individual islands are not. The fact that some of the islands are uninhabited would not lead anyone to claim that "The British Isles are uninhabited".