Yeah, Influence is a bit tricky as it doesn't really function like any of the other characteristics.
I'm at the office atm, do any of the other modules include Influence as a bonus, for example the Highborn?
Personally, I'd just add Toughness instead, to represent the massive amount of physical exercise they went through during their daily drills -- but that is, again, based on my interpretation of the Schola, and I've already outlined my version of the Homeworld stats on a previous page.
So I'd say it's fine if you think that the character's past should have a notable influence (hah!) on the people they interact with. DH2 seems to support a more openly acting Inquisition, anyways.
[edit] Thanks to the internet, it looks as if the Highborn indeed gets a bonus to Influence, so the precedence is provided!
Edited by Lynata