You're correct that I misremembered the requirement; but that's also (counterintuitive as it may be) a requirement that fails in reality; the naive intuition that, even when people view policy on a unidimensional spectrum, their preference for any policy is inversely related to the distance on the spectrum between the policy in question and their most-preferred policy turns out to be far from consistently true.
Median voter theorem also, to be relevant other than in the trivial sense (in which a majority-rule election by definition, choses the formal option which was voted for by a majority of voters, which, assuming unimodal preferences but not necessarily unidimensionality, includes the median voter), requires the substantive policy outcomes to be both determined by the majority-rule election and transparent to voters at the time of the election. As substantive policy is usually indirectly set by aggregate results of of multiple elections that would be, in the best case, majority-of-majorities (but usually is less majorities than that at both levels), and because substantive policy outcomes are often not transparent to voters at the time of elections, the theorem is mostly an empty intellectual exercise.
On top of all that, median voter theorem tends to be even more irrelevant in the US because the US doesn't actually use majority-rule systems as much as people seem to think (it uses plurality rule more often for single-winner elections.)
Median voter theorem is most applicable in the real world in systems with strongly proportional representation, no separation of powers (e.g., parliamentary supremacy), high party discipline, and transparent party platforms that make clear both party positions and relative priorities.
