(not a lawyer) Employment is at will, but there are protected classes. Just like you can not be fired due to your race / gender, disability is also protected - https://www.eeoc.gov/disability-discrimination
Which is why they never tell you why they fire you. They just fire you or tell you that your position was eliminated in a re-organization that only affected you.
Yes, I'm aware, but I personally am in favor of pressing the issue. Though I don't know the details here, in some cases of first diagnosis there will be hospital admission with 72 hour mandatory holding (with limited communication). Instead, consider if someone had been fired for not communicating after being incapacitated in a severe car crash or for the ensuing months of recovery. What would your advice be in that case? What would the companies response have been? How accommodating would they be in the case of the crash?
And yet there are still thousands and thousands of employment discrimination cases every year, even though people doing the discriminating aren't saying "fuck the ADA" while they do it.