Originally Posted by HerkS
The best way to visualize it is to ask "where is the drag produced, and where is the thrust aimed."
This makes sense to me. That is, the thrust should push directly through the Center of Drag. Otherwise, the thrust will create a pitch moment.
The CG could be wildly different than the Center of Drag depending on fuselage design. An example of low CG (which produces a pendulum effect) is C5A. This low CG would not affect the thrust line. The thrust line remains tied to the Center of Drag.