This is mistaken, it does indeed qualify. I'll quickly outline why.
First, the most direct evidence is that the rulebook says so (admittedly I can see why people think that it's ambiguous, they don't use their language consistently). On page 23 selecting chosen powers is listed under "Generating Psychic Powers" and is, in fact, listed before randomly generating powers.
The process is literally this;
- Check to see if the unit entry has dedicated powers.
- If yes, those are the powers you have generated.
- If no, proceed to random power generation.
Secondly, we have some circumstantial evidence. Most importantly there is the Tyranid FAQ which has this gem;
"If the Psyker does not have the Synapse Creature special rule, it gains it for the duration of this power and has a Synapse range of 6."
The Broodlord is the only Tyranid Psyker that does not have the Synapse Creature special rule, the FAQ is therefore meaningless unless you work under the assumption that Psychic Focus works for psychic powers generated by a set list.
In addition, back on page 23, take a careful read through of the example for how psychic powers are generated;
"For example Sarah has a Psyker in her army with a Mastery Level of 3 who knows powers from the Telepathy and Divination disciplines[...] The Army List Entry does not specify that the Psyker knows any specific powers, so Sarah chooses the Telepathy discipline and rolls a D6."
This, in my opinion, shows pretty succinctly that randomly generating powers is a subset of generating powers, not the sole qualification for considering a power to be 'generated'.