> I can't find a source (including 15 U.S.C. § 260a) that supports this reading

From 15 USD § 260a, right after laying out the baseline rule for advancing standard time: “... however, (1) any State that lies entirely within one time zone may by law exempt itself from the provisions of this subsection providing for the advancement of time, but only if that law provides that the entire State (including all political subdivisions thereof) shall observe the standard time otherwise applicable during that period, and (2) any State with parts thereof in more than one time zone may by law exempt either the entire State as provided in (1) or may exempt the entire area of the State lying within any time zone.”

There are places that are exempt from the legal rule advancing standard time, hence, in those places, standard time does not advance.