Bose-X, do you have a reference for that? I searched the whole part 61 text and the only time where "ICAO" is mentioned in this context is in 61.75, which deals with an FAA PPL based on a foreign PPL or higher.
I don't see any reference to "ICAO" in relation to the exception as specified in 61.3.
I fully agree that such a limitation would make sense, though. I just can't see it in the text.