FED: What happens to R1?

[voiceoflg]

I saw this debated on a high school message board. None of the debators are officials, so I'll ask it here.

FED. R1, 1 out, 3-2 count. Hit and run is on but the batter checks his swing on ball 4. The catcher, goes through with the throw to 2nd and BU calls him out (not sure if this actually happened, but I'm just relaying the sitch from the other board). The catcher appeals the check swing and BU said the batter went around. Would R1 now actually be out because the ball clearly beat him and he was tagged out and called out by the 2nd base ump?

Personally I can't see the BU calling the runner out if he saw PU call ball four, even if the batter didn't hold up his check swing. Educate me, please.