Umpire error, or BOO?

[SRW]

3-0 count on B1. Next pitch is ball 4, but neither B1, OC or PU realize it. PU calls 3-0 count, and B1 stays in the box. Next pitch is fouled off by B1. O coach asks PU if that was ball 4 on the previous pitch. PU asks BU what he has for a count. BU says he had ball 4 on the last pitch, and now he has 0-1. They check with the home book, confirming ball 4 was indeed thrown, and the last pitch was fouled off.

Is the count now 3-1 to B1, or do you have BOO to B2 with a non-awarded base on balls?

NCAA, NFHS, and ASA please.

(and no, this did not happen to me. )