Why is this batter awarded a hit?

[apex_pirate]

Here's the scenario:

Bases loaded. Squeeze is on. Batter bunts between 3rd and pitcher. Pitcher charges hard, grabs the ball and sidearms it past the catcher allowing two runs to score and the batter advances to second.

I know the batter is awarded a hit because the out was never made on the fielder's choice to home. My question is why? In my opinion, the fielder had plenty of time to get the guy at first (batter did not beat the intended play) but decided to go to the closest base instead. Obviously the pitcher was awarded an error.

I'm not questioning the legitimacy of the scoring call and know it's been this way forever. Just trying to understand the rational since if the out is made it's a fielder's choice. To me (an amateur scorer) it was a fielder's choice either way. Is it because it isn't clear the pitcher would have gotten the batter since the throw never went there? If so, because the pitcher made a throwing error, why is the batter still awarded a hit? Because the throw was intended to go home instead of first?

[FTMSupport]

This would not be a hit. This would be scored as Sacrifice Bunt, Safe.

[apex_pirate]

Interesting. It was scored a hit in the East Carolina/Marshall game last evening. I figured I needed to brush up on that situation.

[FTMSupport]

If they awarded a hit, it would mean the scorekeeper decided they would not have been able to throw the runner out at first even if they tried. If they got the out at home, would have been fielder's choice. If the runner was safe but they could have gotten the batter, then Sac Bunt, Safe would be the right scoring.