I'm sorry to reply late but I was having picture sending issues and then pizza burning issues and I couldn't type up a comment when I first came across this very interesting topic.
I also have come across a barred white bird in my flock. I have a large and varied flock, he was rather a surprise because I'd never come across one before and didn't realize such a thing could happen. I think that this particular combination of hen and rooster had never come together before, at least not in a male offspring.
For me, the barring came from the hen. I have no barred rooster. My rooster is pictured. He's a mix. My best guess is half Wyandotte, which explains his comb and the lacing on his chest, and half something that is dominant white and single combed, since he does throw single combed offspring on a regular basis. Maybe Wyandotte/Leghorn? The mother of the cockerel is a Barred Rock. I do have a Dominique hen, but to my best knowledge she's purebred and so shouldn't be throwing single combed offspring no matter who she mates with.
We raise our chickens for food and this boy was extra and became dinner in his time, so no further pictures, but it was so interesting to see.