Ah, cool, thank you very, VERY much for posting those references.

The FAA's policy subject to ICAO membership doesn't make it regulatory,
as the ICAO is a standards organization and holds no sovereignty. If a
DOT organinzation outside the FAA, or a department outside the DOT,
adopted those ICAO standards as regulatory, then the FAA would assume
an indirect regulatory role - even so, the equipment requirement would
be arguable (the equipment assumption is for the purpose of determining
minima, not actual navigation, and regulatory equipment requirements
are otherwise very precise). But, as far as I know, this is not the
case.

The second part describes Class I and Class II navigation, but doesn't
spell out an equipment requirement either. On the contrary, it says
that you don't automatically need equipment appropriate for the
corresponding class of navigation.