Yes that's right, you'd probably be fine with normal physiological doses of steroids (eg, hydrocortisone 15 mg daily). But if you you use supra-physiological doses like hydrocortisone 80 mg (equivalent to prednisone 20 mg or prednisolone 20 mg) during an acute viral infection, that might cause issues. (I forgot to look at the doses you actually used).
Dr Chia found that giving supra-physiological doses of corticosteroids during the
acute stage of enterovirus infection is actually a recipe for creating ME/CFS. See
this post. My guess is that the immune weakening that corticosteroids produce with respect to the antiviral response lets enterovirus get the upper hand during its acute infection phase (the acute phase is the first week or two of infection), which then paves the way for the chronic enterovirus tissue infections which some researchers think cause ME/CFS.
Taking a short course of supra-physiological doses of corticosteroids during the chronic stage of enterovirus infection when ME/CFS has already appeared is less of an issue, though there are reports of ME/CFS becoming worse after patients have taken supra-physiological doses for a few months.