Tthat is not a "definitive truth. Falsework is needed on site when concrete is used in situ. If there are in situ concrete elements, like, p.e., the towers, falsework may me needed.
But yes, the most commom suspended decks don´t need falsework as, after erecting the towers and eventually the erection cables, the main catenaries are assemled, the hangars are erected, and the deck segments are lifted or slided to the place (completly different than cable stayed bridges - both the structural systems and the process).
This kind of (simplified described) deck erection does not need falsework.