As explained in the document referred to by thesun, the DOT requires "each U.S. and foreign air carrier that has a website marketed to U.S. consumers post its customer service plan" committing to the DOT's 24-hour reservation requirement. If you purchase tickets from Icelandair's U.S.-facing Web site, the DOT rule applies regardless of the route -- whether entering, leaving, or even wholly outside of the U.S..

Icelandair claims that their Customer Service Plan applies only to passengers "with point of origin departure in USA," but the DOT rule has the effect of law in the U.S. and overrides any limitations or stipulations that an airline might place on the DOT's 24-hour reservation requirement.

If you receive any pushback on this issue in the future, you can file a DOT complaint to give the DOT the opportunity to intervene on your behalf.