Hi FD,
Not entirely true. Whilst what you say gives an acceptable result in most cases, it could start a shallow descent too early, primarily if an excessive decel rate is present (hot/high/heavy).
The way the AP/FD manages the pitch change in OP CLB/DES (speed on elevator) is a sacrifice/exchange ratio between kinetic vs potential energy.
Likewise if you pull OP CLB in the EFATO case (third segment), before reaching Green Dot, the a/c will start a shallow climb in the level segment: Accelerating and climbing at the same time in accordance with the ‘energy ratio’.
So: pull ALT when reaching Green Dot, not before.
brgds
s