Well
You can't just read the current 2257 regs to get the full meaning.
Above (b) the "picture ident card" is only needed when the model does not have a proper "identification document".
Identification Document is defined in 18 U.S.C 1028(d)
"The term 'identification document' means a document made or issued by or under the authority of the United States Government, a State, political subdivision of a State, a foreign government, political subdivision of a foreign government, an international governmental or an international quasi-governmental organization which, when completed with information concerning a particular individual, is of a type intended or commonly accepted for the purpose of identification of individuals."
So a "picture identification card" comes into play when the record holder does not have records that fall within the meaning of "identification document".
So having a passport with a photo id, which is issued by a foreign gov, is fine.