Has that been true of all thee people who learned Icelandic? 
Speaking as the Icelandic-American child of an expatriate Icelander and as someone who took some linguistics classes, I think I can expand on this with some accuracy.
I firmly believe in the Sapir-Whorf hypothesis, which states that the language one speaks shapes the way they view the world. I’ve seen it in action within my own life and within others, as language is intrinsically tied to the culture that invented the language. It’s why we get such fun but morbid words for concepts that we have to explain in long phrases in German and why some concepts are completely rendered mute when translated from their original language to another one. Language helps define the culture one lives in and gives us cues to societal standards, and when language from other languages leaks into a language, it changes the way those speakers view the world.
Icelandic is the closest language in the Scandinavian language family to the original Old Norse, and its reflected in our worldview. We still hold on to a lot of our old values and we can use old words to describe new technology. For example, sjónvarp is the Icelandic word for television. It has a connotation of the tv being more of a passive experience, which it is. I don’t necessarily see that connection in its English counterpart, or telephone for that matter, which have a bit more of a formal connotation because of their connection to Greek; we have no personal connection to the words that make up these words. When language changes (and it is in Iceland, just not necessarily in the written form), the cultural ties to these now excluded words lose significance within the culture. It’s not about some sort of bigotry or hatred of other cultures, but of a love of one’s own culture and wanting to preserve and share the magic of being within an in-group’s understanding.
English is kind of like a bullying imperialistic monarch who stole from other languages to attain some sort of prestige in the past. It’s borrowed a lot of terms and concepts and there isn’t necessarily as solid of an identity as languages who’ve been less involved in other cultures. There’s also an element of it infiltrating and changing other cultures to make it more like English, which inherently causes a loss within those cultures. It does make me feel sort of odd when I see how much English has infiltrated other languages; Japanese certainly has picked up quite a few words with no attempt to adapt these concepts with their own available vocabulary. Then again, do they have compound nounbuilding as part of their language? There’s got to be a better way to say “smorgasbord/buffet” in Japanese than “baikinga” (a moderate bastardization of the English word “viking”).
As far as languages go in Iceland, students learn Danish, then English (and then inevitably they pick out a third foreign language to learn in high school) in school. Why Danish? Well, Denmark and Norway spent many centuries ruling Icelanders, and the Danish were the last group to really hold much sway, so we more or less were bullied into this system. It happens, but it (strangely enough) makes learning English easier for a lot of Icelanders, which helps Icelanders better interact with the world around them. It doesn’t, however, mean that they’re necessarily going to eschew their culture entirely for the sake of cultural assimilation with foreign countries.
What’s really funny is that Old English is extremely familiar to me because of my knowledge of Icelandic. It looks pretty similar and isn’t that distant from Old Norse.
Not necessarily, but it’s definitely true with people who move to Iceland, learn the language, and actually live by the cultural rules present in Iceland. There are a number of Icelanders of Asian descent who fit in with the culture quite well and don’t have any problems with Icelanders of Icelandic descent because they attempt to live within the cultural rules of Icelandic society. On the other hand, there are quite a few guest workers from former Soviet Union countries that are causing quite a ruckus via importation of drugs, increases in criminal acts by said guest workers and a general refusal to learn either English or Icelandic in order to communicate better with the natives. They’re also abusing the social welfare system. It’s drastic enough of a problem that there are serious considerations toward deporting them.