I assumed that what taurath meant is not that he or she couldn't stay home, but that they couldn't be truthful about why. Your solution finesses that with ambiguity, which is fine if needed, but what if people really could just say what they feel?
"Not feeling well" is honest though broad. People shouldn't feel bad about telling their boss that. Bosses should feel bad for prying for details. The only point of that would be to judge whether the specific problem is a "real problem".
The typical policy these days is to transfer the employee to some sort of disability after certain patterns of absence (X days in a row, Y days over period Z). I feel that is a good compromise. It's also very good for small teams since it's a predictable insurance payment, not a risky hire.
I guess the question is why you need them to know. I can think of a million other legitimate medical reasons that I'd never put in an email to my team. Why is this any different?
Also, you should consider that if everyone gets away with being consistently vague, you set a team standard that says people can stay home whenever they feel bad, for whatever reason, and it becomes harder for the company to legally crack down on someone who's doing it for emotional or psychological reasons.
Feelings aren't medical reasons, they're core to being human. If we cut that off from how we're allowed to be in the workplace, we can't really be ourselves. That causes problems. Imagine if people wouldn't let each other breathe properly. That's analogous to where we are with emotions at work.
Integrating feeling into the workplace doesn't mean sharing every emotion, any more than you'd share every thought or every story about your life. It just means being able to accommodate that information when it's relevant and respond appropriately, instead of seizing up with a taboo reaction. Then we'd trust each other more, be more creative, more satisfied at work, and so on. This would be good for productivity, so the most ruthless capitalist ought to be in favor of it in the long run.
But I think my comment may not have been clear. I'm imagining something that I hope will be possible in the future. It clearly isn't broadly possible at present.
Indeed, the social contract of the workplace is mostly still way too rigid for that to work. I think it's changing, but slowly—similarly to how the stigma around taking a nap at work has is gradually wearing off.
