Stierlitz refused version with Twilight because of three reasons. Firstly, despite of her status, Twilight has no real political weight in Canterlot. She has little to no popularity neither among the military — even if she is a close relative to Field Marshal Armor, neither among the party members, neither among the Secret Service personnel.
Secondly, she is a figure with too much publicity — and for such business too much publicity is a no-go.
And thirdly, she is fanatically devoted to Celestia.