That is still puzzling! He definitely has white barring, and if the father (Rhode Island Red) had no white barring, then it must have come from the mother. So I think his mother must be the Barred Rock (even though that means she is carrying some genes that a purebred Barred Rock is not supposed...
Your logic all seems correct to me.
I see two possible answers:
1) It could be a pure Rhode Island Red. Sometimes they get odd patterns in their feathers when they are young, but later mature to have a nice even red color. I think this is the more likely explanation, even though I have not seen...