Does brilliant need to be quantified?
Of course there's her background, but 1) that doesn't require anyone to know her and 2) it means she's successful, which may or may not mean she's brilliant.
Perhaps I'm just jaded by years in a BigCo. All a high position means to me is that they're "brilliant" at politicking and networking. (And staying silent in this case may be an example of that "brilliance").