Again, they should tell their clients that they should contact the administration. They should also have a list of alternative sources of help in the short term. Don't be naieve. Unless the faculty member can establish that the illness occurred before the strike, the administration has every reason to suspect that such an illness is a pathetic attempt to placate both sides. It will do neither.
Management has the right to a doctor's note after three days of sick leave.
But, there will be a picket line at or near the stadium. He would be violating the picket line to direct the band. We have spoken with Frank DeStefano, but not about this issue. The union members of touring companies would need to be informed that there is a strike, and that to perform, they would have to cross a picket line. Student may also not use laboratories or studios if they are not under appropriate supervision, again, for again reasons of liability.