Always pot holes. HIPAA would not cover anything you revealed about your health to the general public. However "general" would need defining if action against your employment were to occur. Confidentiality would have a point of discussion. SSDI would likely come up if a legal conversation took place. ADA is different. You may only be released if you are unable to do your job with reasonable accommodation being made for you (i.e. keep cf students in other classes). As for hospitalizations, likely no school grounds there (it is reasonable to have subs). Is there board of education liability from you suing them if a student gives you "something" (provable)? Noone would have a case against incidental H1N1.
I do not think you should start a conversation in this. The comment of you giving a student "something" (as your physician seems to say) is untenable as soon as there are 2 cf students unless home tutoring comes up. Let the administration start the conversation. I suspect board legal counsel will say "be quiet" to them unless you bring it up. Be positive about your teaching value only. If you are asked, I'm not sure there is legal grounds for them to know unless they have a board counsel directive; in which case you may say you have no need to reveal your health concerns (lawyers learned about this in the context of AIDS discrimination). That is where the ADA came from initially but then became all inclusive (such as wheel chair bound conditions). Discrimination in any form is expensive in any school so I think if "it" comes up, then get a lawyer or ACLU. Or maybe the CFF, Esiason foundation, etc have a legal solution.
There is always the presumption of "administration recrimination thinking" but that's going negative to your concern. I suspect the administration is covering it's base (if in fact it is legal to treat you differently from the rest of the faculty with regards to annual vs tri-annual physical reports/health updates ). You are obviously a positive element on the faculty and just remember the glow you bring to the classroom and faculty room. You do not need to stay awake thinking of rebuttal when there probably won't even be a mention of this.
Good luck, don't volunteer what hasn't happened. If you go back about 40 years, the Readers' Digest had a story about "Do you want to borrow a jack?".<a target=_blank class=ftalternatingbarlinklarge href="http://home.earthlink.net/~twc8453381554/cathphil/id196.html">Story</a> This is sort of like it.
Peter