The faint connection rests on the medieval idea of the estates and their relation to one another.
Under the medieval ideal, the peasants, merchants, nobles, and clergy (like the corporatist bodies under syndicalism/fascism) all occupy different but complimentary roles in society. The noble's job is to defend the land the peasant and the monk work and the towns and roads the merchant uses from invasion and bigandage. In exchange for agreeing to pledge his life and honor, he earns the income of the lands and the right to collect taxes from peasants and merchants. Each class depends on the others, each class has responsibilities toward the others, society is an organic whole.
However, this ideal is based on the notion of subsidiarity. There is no absolute ruler or state - power is a web of personal allegiances, treaties, inheritances, contracts, etc. There is no "nation" and there is no "leader" and there is no notion of unitary power or what we would call sovereign government in the modern sense.
The medieval Church was radically libertarian in many ways, and highly authoritarian in others - but the emblem of medieval government was the Emperor: an almost powerless figure whom everyone in theory swore allegiance to.
Thank you again, wideawake.