Feeling ill and the doctor's responsibility

Everyone has a bad day from time to time. I wasn’t feeling very well when I went to work today, afternoon shift. I went nevertheless, but was a bit blocked and stuffy. I usually have about one or two days like this per year, and frequently it’s on my day off.
Normally I would have an aspirin (in fact I did before leaving home) and just work through it. But during this last year I’ve seen too many incidents to be working without being 100% fit. And you must consider that in my current situation I’m not even the last person responsible for my sector, because I’me undergoing instruction in order to recover my validation after a long leave.
So, I decided to go to the workplace doctor. She’s upstairs from the operations room, less than a minute. I explained that I wasn’t feeling tiptop and she answered that she needed objective parameters. Temperature wasn’t too high, 37,2; and a visible sore throat wasn’t enough. So I had a chat and I tried to convey that the only real way to guarantee maximum safety is to make sure people who are not feeling fit on the day don’t get to work at their sector. It’s a very complicated issue, and once again the debate is upon the limits. The doctor admitted to not being able to know objectively if I had a headache or not. I didn’t, and I really just thought I should be relieved based upon not feeling very well, nothing else.
It turns out that the doctor doesn’t know what an airprox is. (You’ll excuse me for not knowing English jargon for that: literal translations from Spanish are crushing, sanding, or shoving). She has never been in the operations room. She doesn’t have a clue what our job is about. I assumed the doctors are pressurised upon to give as few leaves as possible. She denied it. Finally I stated my opinion that not everything could or should be objective: if a controller isn’t feeling fit, he/she should refrain. There are rules and fines for faking illness, but what about a headache, your dog died last night, or you exceeded yourself in the jogging and you’re sugar’s running low?. These can’t be judged objectively by simple visual examination by a doctor. But they are limiting conditions. So how should it work, because, on the other hand, I admit we can’t have workers pulling out ill whenever they want a day off (although this is a lesser evil).
In the end, the only way to organise this is to base the employer/employee relationship on confidence and good will. And throw in a couple more controllers than are needed in the shift, just in case.
By the way, I finally had high blood pressure, so I did leave for home. The doctor had to fill in five sheets of paperwork (isn’t that pressure against the leave?) and if I want my report –which I will- I have to go through a rigmarole involving the operations room Head and the Human Resources department. And I’ll get my report in a couple of days!
If you’re a controller from abroad, let me know how you do it. In comments below or to simon.a.rance@gmail.com. Thanks