EXCEPT (and there always seems to be at least one exception in these rules and codes!), the Supreme Court of Idaho has ruled that Public Defenders offices are not firms within the understanding of 1.10 of the code, since they are not for profit nor financial endeavours. As I'm sure has already been stated here somewhere, possible COI imputation to an entire public defender's office is performed on a case by case need, and there must be clear concurrent conflict of interest with other lawyers in the PD office. With the appointment of a conflict defender to replace AT, there is no concurrent COI, IMO.
The case that set this standard is itself interesting in light of BK: a man convicted of murdering his wife claimed after the trial his PD and the entire PD office had a conflict of interest because someone in that office had represented the mother of the victim. The mother's case was a civil matter seeking the life insurance of her deceased/murdered daughter and depended on finding the man guilty as the slayer. That case appears to have far more conflict of interest possibility than BK and AT, yet the courts found there was none because the man himself admitted he received an adequate defense.