When there are 100 blue-eyed islanders, the correct statement is that “everyone already knows that at least 99 blue-eyed islanders exist, and knows that everyone else knows that at least 98 blue-eyed islanders exist, that everyone else knows that everyone else knows that at least 97 blue-eyed islanders exist, and so on”, with this chain of knowledge terminating after 99 steps. The foreigner adds the crucial 100th step that starts off the chain reaction. (If the foreigner asserted that blue-eyed islanders existed to overlapping proper subsets of islanders only, then it is indeed true that no new information is added, because the information content of each of the foreigner’s statements does not reach the 100th level of the hierarchy.)

As I said in my previous comment, one has to continually distinguish between truth and knowledge at every stage of the hierarchy in order to obtain a correct conclusion; in particular, when there are k blue-eyed islanders, one has to make this distinction k times (and not just once or twice).