Vjoe - I have no issue with people disagreeing with me about what is happening in certain exercises, however I think you might be misinterpreting Westside's view on the subject. They way Westside suggests squatting, and all deadlifts, those movements are posterior chain dominant (which is the erectors, glutes, and hamstrings). Westside and Louie Simmons do believe that deadlifts hit the erectors pretty hard, here are two quotes from him in an article he wrote about how to train the deadlift:
"Squatting with a bar held in various ways will place the stress on the erectors, hips, and glutes; the primary muscles that deadlift."
"If you do all deadlifting, it is a matter of time before your deadlift will stall, or even worse, injury will stop all progress. Why? No ones body will equally distribute the work evenly between the lower, mid, and upper back. If the lower back takes the major role in deadlifting, which is most often the case, eventually an injury will occur."
Westside combines those movements because they have a carryover effect on each other and because the muscles are pretty similar, separating them out would be too much for one to recover from especially since their philosophy is train each movement twice a week. Hope that helps.