I always assume that in a situation like that, 4th and 1 to close the game out, that the Head Coach is involved in the play call. They likely have four or five "go to" plays there, and to me the Head Coach should be the one deciding how the game turns out.
I can see the "trust your coordinator" argument, maybe they are already aligned philosophically pre game, but if I'm Eberflus making that call I wouldn't make it by saying, "take your pick," I'd say something like "QB Sneak", "QB sweep",
I mean they took a time out, so there is plenty of time for Getsy and Flus to discuss the play call. To me the play is on Eberflus more than Getsy