(Edit: See update comment below)
I emailed Sarah Constantin about this question. I didn't end up hiring her (my parents decided they didn't want to take supplements--luckily they're working from home now), but she did say:
BTW, the apparent "contradiction" isn't really one. Immunostimulants, taken when healthy, reduce the incidence of respiratory tract infections; once you get an infection like COVID-19, the immune response often gets so strong it kills you.
So I think taking immunostimulants on an ongoing basis is a good idea, but you should stop if you think you might be infected with COVID-19.