You are right. Coups almost never are the lower ranks rising up but a handful of high ranking officers and elite military units backing them. It's elite units like modern special forces loyal to a specific high ranking military commander that end up the muscle and shock troops for coups, the storming the presidential palace and congress buildings taking the government into custody. Their elite status is what keeps the rank and file military along with law enforcement from making serious efforts to get in their way.

Just look at how it often goes down over the last few decades across Asia, Africa, and Latin America. Even funnier when you find out many of those special forces units were trained by US special forces. This isn't new and goes all the way back to the Roman era, when the elite Praetorian Guard units would regularly be the get-your-hands-dirty muscle for coups.