That was true a few decades ago. Demand for tourism jobs has outstripped supply (especially in summer months) so a good number of people have come to Iceland (some temporarily, some permanently) to work. Poles are the largest group, making up about 5% of the population of Iceland: https://en.m.wikipedia.org/wiki/Poles_in_Iceland
Anecdotally, on a recent trip I briefly felt like there were no Icelanders in Iceland - I had a British masseuse, a Finnish horse tour guide, and a Namibian scuba guide.
Yeah Americans seem to have gotten the idea that nordic countries are completely homogenous for some reason. It's absurd how often I see them act like we can't compare our countries to the US because we apparently have no immigrants.
In the US there are many ideas about how things work in Sweden without closely considering facts. This is often politically motivated regardless of political affiliation.
They aren't, but Scandinavia may as well be. The only land border is an icy, barely-populated taiga controlled by an extremely authoritarian, violence-happy enemy of the West. My bet is crossing that border is _significantly_ harder than the US-Mexico border
In most cases you have Icelanders running the tourism business, but they won't be fronting the business necessarily. That is where imported labour comes in.
Anecdotally, on a recent trip I briefly felt like there were no Icelanders in Iceland - I had a British masseuse, a Finnish horse tour guide, and a Namibian scuba guide.