Sometimes an app doesn't seem to be suspended completely and parts of it keep running. A few years ago the Facebook app was notorious for this: if you didn't force-quit the app it would often suck the battery dry in a couple of hours. This would happen sometimes even with apps that were not designed to run in the background, i.e. track your location or keep an ear out for certain events. But those few cases aside, the guy is right: in almost all cases it makes no sense force-quitting an app; just going back to the home screen will make it suspend all activity. And over the years iOS has gotten a bit better at suspending apps.
App developers have to do very little to make this happen: threads are stopped automatically after a while, the app gets notified so that it can wrap up stuff and save the device state, free up memory if possible, and so on. And even if you don't free up that memory like a good little boy, the phone will do it for you... pretty much by force-quiting your app when needed. Not ideal, but as a developer you have the choice of either releasing memory or just let the app die when the phone needs it.