You have a point, but I am not sure that this is a complete analysis of the situation, because it does not consider the changing moments as the centers of press

You have a point, but I am not sure that this is a complete analysis of the situation, because it does not consider the changing moments as the centers of pressure of the wing and stabilizer move in response to the changing airspeed. Furthermore, when one moves the elevator of a subsonic airplane, it does not just change the force generated by the elevator, but also the force generated by the stabilizer it is attached to (by affecting the airflow over it), so that is another potential source of changing moments. Perhaps the phrase "aerodynamically relieve the air loads" means to minimize the aerodynamic force generated by the stabilizer? The stabilizer of a conventional airplane will invariably generate a downwards force when the aircraft is in pitch equilibrium at high speed, but it may be upwards at low speed, even with the C of G within limits. In such cases, the speed at which it has no load will be an intermediate one, and therefore could be either above or below the speed to which the airplane is currently (mis-)trimmed. The quoted passage says it is referring to correcting what it calls a mis-trim, so if your interpretation is correct, then where it says "in-trim speed", it actually means "the speed to which the airplane is mis-trimmed", while the general usage of the term "in trim" means trimmed to fly at the intended speed, and I would take the phrase "in-trim speed" to refer to that speed - the speed that the pilots intend to fly at, or, in other words, the speed that this out-of-trim airplane would tend to fly at when put back in trim. Furthermore, if things are as you describe, then the rule could have been more simply and clearly phrased as "reduce your pressure on the control yoke". Maybe your interpretation is correct, but if so, it seems to me to be an unnecessarily confusing way to describe it.