False. During conservatorship they don't have fiduciary duties to any shareholders, common or preferred. And once the fiduciary duties are restored they will apply to all shareholders, common and preferred.
That's Ackman's thesis, and he has hedged with quite a few prefs in case he is wrong. The specific phrase he used was "it hedges our risk of a restructuring that disproportionately benefits the preferred versus the common shares". He knows that's a possibility even with Treasury's warrant stake.
Just be careful of an outcome like Treasury selling the warrants to a third party, at which point they will no longer care about the share price, or Treasury converting the seniors to commons, when their interests suddenly oppose those of current common shareholders.
Also, Treasury trying to maximize its return does not necessarily mean trying to maximize the common share price. If they just want the most money possible they will monetize the seniors, which would crush the existing commons utterly.