Yes, I think we've talked this one before and it is somewhat symantics. Fielder's choice is only defined in OBR to account for the advancement of runners because of the decisions of fielders.
The most common fielder's choice situation is defined in 10.05 b The official scorer shall not credit a base hit when a...
(3) pitcher, the catcher or any infielder handles a batted ball and puts out a preceding runner who is attempting to advance one base or to return to his original base, or would have put out such runner with ordinary effort except for a fielding error. The official scorer shall charge the batter with a time at bat but no hit;
You give a FC to account for the runner reaching first, but score AB and no hit because of this rule (not because a FC is an 0-1).
It works the same way with a sacrifice. The batter gets a sacrifice because of 10.08 SACRIFICES
The official scorer shall:
(b) Score a sacrifice bunt when, before two are out, the fielders handle a bunted ball without error in an unsuccessful attempt to put out a preceding runner advancing one base, unless, an attempt to turn a bunt into a putout of a preceding runner fails, and in the judgment of the official scorer ordinary effort would not have put out the batter at first base, in which case the batter shall be credited with a one-base hit and not a sacrifice;
The FC simply accounts for why he's on first and not out.
If you search OBR for fielder's choice, you can see that its more of an accounting for runner advancement than a definition of an at bat.
OBR