Ah, I believe this is a very unfortunate typo in the book; from the semiofficial Lancer FAQ:
Core Bonuses Errata?
The text currently reads “These ranks can be in any combination – for example, you might have the rank I and rank II license for one mech and three different rank I licenses, equaling six in total.” This should instead read “These ranks can be in any combination – for example, you might have the rank I, rank II, and rank III license for one mech and three different rank I licenses, equaling six in total.” Each rank in a license counts once, regardless of whether it is rank I, rank II, or rank III of its respective license.
You can see it working like it does in LT in COMP/CON, as well.