The outer triceps
Myth: Triceps press with reverse grip is building up the outside triceps part. Practical example: The upper arm is held next to the body. With pushed through arms the hands are moved from reverse grip to malleus handle grip to upper grip. If you look over your shoulder into a mirror you can see that the tricep muscles dont change their from does not change its form.
The same can be done with the biceps. If when straining your biceps the hand is moved from lower grip to malleus handle grip to upper grip. Here you can see that the form of the biceps and with it also the strain for parts of the muscle changes,because it is linked to the forearm. The biceps is used for lower grip, malleus handle grip strains the brachial muscle and the upper grip is mainly done by the brachioradialis.
(source: c/o Freie Universität Berlin (Free university Berlin), https://www.kenhub.com/en/library/anatomy/biceps-brachii-muscle)
The triceps cannot be changed in form due to changing grips and with that the recruiting muscle cannot be changed, which is due to the fact that all three parts of the triceps have their origin in the forearm (tendon marked in light blue).
For that reason when doing triceps pull ups with lower grip the outside part cannot be more strained than doing it with an upper grip.
the following test proves the observation: If the entire exercise is done only with lower grip, the muscles that are sore, are only the ones in the inner triceps parts.
In your shoulders however, the triceps muscles are linked to different parts: the inner triceps (green) at the shoulder blade, the outside (purple) and center part (orange) at the upper arm. For that reason the change has to start in the shoulder joint in order to recruit the outside triceps.
In my book you can find out how to mainly use the outside triceps.
The problem of the latissimus
Myth: Lat pull-down exercises mainly use the latissimusmuscle (green).
In the research work of the Canadian Memorial Chiropractic College, it was found out that doing rowing exercises would have 40 % higher muscle activity than doing lat pull-down exercises with wide grip handle.
The result was clear, if one is doing lat pull-down exercises with a wide grip handle and pull ups the teres-major (red) and the lower neck muscle (light blue) are mainly used.
The teres-major is the muscle that is often thought of as the outer or upper latissimus by a number of athletes, but is its own muscle. To build this muscle is very important for the upper width of one's back, no matter if it is for the rear or front view.
If one looks at anatomy, one will see, that the latissimus is twisted in itself and the teres-major is moving around it, which results in the fact that a certain motion sequence is necessary.
(source: c/o Freie Universität Berlin (Free University Berlin), https://www.kenhub.com/en/library/anatomy/latissimus-dorsi-muscle)
In my book you will find out how the latissimus is mainly used.