Boundaries

Recently, my dad sent an e-mail to the lit band that he runs at the school he teaches, and by mistake he signed it his first name instead of his last. He quickly sent a follow-up email saying "that's Mr. last-name, opps." He is now worried that the school will think that he broke the boundary between students and teachers, and that he may lose his job.

Is my dad's worry unfounded, or is this something to be legitimately worried about? I don't think so since it's the only time he did it, and he quickly responded to his mistake.