CoS Auxilliary dteachment and access to CoS stratagems

Lets imagine an army list with a Realspace detachment with CoS wyches and a lot of good stuff.

Then you want to add Drazhar to the party and take an Cult of Strife Auxilliary dteachment with Draz only.

The wording in the supplement says that you can use the strats, if you have ANY CoS detachment. But as far as I remember the Aux detachment doesn't unlock specific strats for you. Or it does in this case?

The Codex specifically excludes Auxilary Detachments from who gets access to stratagems, so if you take a CoS Auxilary it doesn't give you their stratagems.

EDIT: Realizing now that the Book Of Rust didn't include the "excludes" part, I would wager that is a typo to be errated. In any case, I could see Tos ruling in line with the Codex version anyway.