Since the meeting with the campus community was called to discuss such matters, the faculty member should speak up in the course of the meeting. However, if the board's actions are not on the public record, and the faculty member is relying on non-public information, different considerations arise. It is well to remember in matters of this sort that both the budget and policy making processes in public universities are complex. Further, a decision that some may think is being driven by budget considerations may be happening pursuant to policy and vice versa. Therefore, the faculty member should consider that what seems to be so, may not be so.
Discussion is the way to find out.
The fact that the program being discontinued oversees required courses may not be relevant. Many programs offer such courses which enrich the curriculum, but in spite of what the faculty who teach or support them may believe, few are indispensable. The goal of the faculty member, I assume, is to maintain funding for the program. One likely result of publicly correcting the lie is that of antagonizing the administrator. Indeed, embarrassment could force the administrator into a defensive, entrenched position on de-funding the program.