I think we are both right. Armies that have a ?Brilliant? C-in-C have access to stratagems other armies don?t have access to. These have to be paid for before deployment, using AP?s. However, the sentence implies that if you use one of your brilliant strokes you can use a stratagem that you did not have access to before deployment, or one not paid for, and therefore does not need an AP cost when activated. Why else would that section say that ?a Brilliant C-in-C can expend a BRILLIANT STROKE to SPECIFY a STRATAGEM OTHERWISE NOT AVAILABLE??
The implication could be that a Brilliant C-in-C could use a brilliant stroke to say activate a ?Feigned Flight?, which the Brilliant C-in-C could have paid for before deployment but may not have done in order to use another stratagem, or to activate a stratagem it could not have used at all, such as ?False reinforcements?.