Bunted ball contacts bat twice

[officialtony]

FED Rules. 1 out, R1 and R2. Batter bunts at a ball which goes straight down to the plate and bounces straight back up, makes contact with the bat a second time, and rolls out in front of the plate in fair territory and stops. Batter was in the box when the ball hit the bat a second time.
Please help with the call here.
I'll give you our at-the-time-of-the-play decision now.
We allowed it was a fair ball ( PU signals fair ball ), B/R runs to 1st. F2 makes a terrible throw pulling F3 off the bag and B/R is called safe. Defensive coach says B/R should be out for hitting the ball twice. PU and BU rule no intent to hit the ball twice, bunted ball became a fair ball by definition, play on. Resulting play stood. BU and PU conversed privately and decided that since there was no intent to hit the ball twice ( our judgment ), the play was live and the ball was fair.
When I returned to my vehicle, I checked the book and only found 8-4-1d which clearly states intent the reason for the batter being out. We ( at the time ) felt there was no intent and thus let play continue. Did we misinterpret 8-4-1d? Or is there another rule to cover this?
Thanks in advance.