Why did Vis say he would pledge governance if he lost foundation

Im mainly making this post after the announcement of the release of the second book. I always though Beli was in Military because of the fact that she went to Suus with Vis Emmisa and Indol because it was a millitary family only summit but then to get into class 3 (on page 505) why did Vis say he would pledge governance if he lost in the game of foundation.

Quoting he said it would "Raise Beli's stock inside governance as well as in here" Why would that attract Beli if she wasn't in Governance the first place and why would she agree if she was from Military?

Is it like Beli's mothers from Military and Belis father from overnance type of thing or was it a known fact that she was going to change her loyalty