Let me start by saying, "if you are sick, call in sick!" Don't fly sick. Any day and time, use your sick time when you are sick.
Now the other side of the story: why do employers ask for notes on holidays? Because pilots too junior to get the day off call in sick- when they are not sick. Sure, you can be sick on a holiday, but we all know the sick calls spike around holidays, superbowls, weekends, snowstorms, etc. Ask any reserve pilot. They will always work the above days. You think you're sticking it to the company, but in reality, you are screwing a fellow pilot.
If you're sick, call in sick. If you're not, work your own pairing.
Yes, I'm on reserve.