Yes, I agree the claims that "Iceland's medical infrastructure is at its limits" are exaggerated. Iceland's population is 357,000 people. Bolton (which is roughly 200,000 people) right now has got 45 patients in hospitals and 5 in ICU. The winter peak was 161 patients in hospital and 19 in ICU. Iceland's numbers of 20 and 5 are clearly very low.
However, even if we disregard the healthcare claims, the main point of the article still stands - even countries with very high vaccine coverage (like Iceland or Malta) are still seeing Delta waves. Spikes in cases are unavoidable. It is also inevitable that they will be followed by hospitalisations and deaths but, hopefully, at much, much lower levels than previously.