What was once thought to be imagined maladies are now known to be attributed to the air we breath indoors. In fact, as many as half of all illnesses are either caused or aggravated by indoor air pollution. According to the EPA, indoor air can be up to 70 times more polluted than outdoor air. Inadequate ventilation is usually pretty straightforward to fix. Building operations personnel have little or no control over external pollution sources and usually must resort to special filters or other solutions.
Internal pollution is a little easier to deal with, especially a contaminated duct system.
Ignore the problem. Hire a duct cleaning contractor at considerable expense. Acquire the necessary equipment and training to perform duct cleaning in-house. Ignoring the problem is foolish given the litigious nature of the times in which we live. No educational or health care facility wants a lawsuit over a situation that could have been addressed and corrected.