I haven't read that particular post you refer to that recommends avoiding consumption of anything with faces, but all I can say on the subject is that: I don't think that fish can be properly classified in that group, as they don't have "noses", technically a prime requisite for qualification as a true "face."
Also, fish are pretty much devoid of saturated fats, although I don't know if that has anything to do with them not having noses.