I think by "type level" @andrejbauer meant "homotopy/truncation level", not universe level.  If these were the constructors of a HIT and there were no separate truncation constructor, then they could make a difference there.  Without a truncation hypothesis, they could also cause the type of precategories to have the wrong homotopy type.  But as @JasonGross pointed out below, the assumption `MorphismIsHSet` ensures that all the morphism-types are sets, so that equalities of morphisms are unique whenever they exist.  So I don't think there is any problem.