There is no reason why an icon can't be skeuomorphic. Flat design was inspired by Swiss design, which really only existed because of technical constraints of graphic design in the 50s and 60s.

An icon should indicate what the program does, and with higher quality displays, there's no reason why more detail in the icon would be worse. Icons aren't logos in the sense they have to be adapted for every possible use case (where those use cases may have technical limitations), e.g. on a huge box truck, embroidered on a shirt, or as a favicon.