I was under the impression that the policy needed to be companywide. My boss is just upset that it was on an inconvenient day, so he's trying to "stick it to me".
You're mistaken. If the boss wants a doctor's note from you and only from you, he can require that.
I guess I have to make a decision now whether my morals or my pocketbook are more important to me.
This hardly seems something worth losing your job over. Unless you're independently wealthy, I suggest you see a doctor.