Step 2 from the rulebook explaining the build action is as follows:
Play cards from your hand until you have paid the amount of
Labor shown to the left of that structure on the player mat.
At least one of the cards you use must be from the faction of that
structure (unless building on the General structures tree). Any
additional Labor is left unused.
For example, I want to build a Black Gulag and use 4 labor from green and yellow cards and then include a Fist of Zurd which has 0 labor, but is a black card to meet the faction requirement. So the Fist of Zurd is used in the build action and can't be used for any other actions in the turn.
This to me is fine - you are sacrificing playing the Fist of Zurd card in another action during your turn to meet the requirement of building the structure. Nowhere in the Build action explanation does it state that the card you play to meet the requirement actually needs to have a labor value.