I don't think you need to divulge any sensitive details, but unless this is a "one in a million" occurrence, it's possible that others might be faced with a similar situation in the future, so it might be useful to share at least some broad details. Was HR concerned that it would lead to legal problems, e.g. an ADA violation or a claim of discrimination against a protected category? Or was it more like a nepotism issue? As a manager, I would likely handle those in different ways.

You've lost the trust of people reading this thread just as much as you lost the trust of your team when you couldn't find a way to be appropriately transparent with them. For a problem that affects them daily, you can't really leave it at, it just is what it is.

You can say there was a medical issue, or a discrimination issue, or nepotism. If you say nothing, people have to assume the worst.

The worst in this case is probably people assuming you didn't try very hard to fire them.