Ultimately yes - but not at grant time, just like how a CEO is responsible for everything in a company either directly or indirectly. Shit flows up, he may not be personally involved in the decision but he absolutely has to be briefed on it (or know who to ask) if things go sideways so he can answer to Congress/President (just like a CEO to the board).

If congress starts calling him to the floor about those fellowships, he'd better make sure to know about those too, yes.