Was it incumbent upon me not to tell them the truth and resort to "concealments" instead, in the incident of the loss of the student's answer sheet, which led to my being accused of knowing the student and doing that so he would pass?

The basic principle is that a Muslim should only speak the truth. However, lying is permissible to protect a Muslim from harm, while striving to use Tawriya (double entendre) and Ma'areedh (allusions). The president should have been informed to bear responsibility. There is no harm in apologizing to him to resolve the issue. It is recommended to persevere in acts of obedience and Adhkar (remembrances).