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.