It's not a storm in a teacup at all. A lot of us don't want to be seen.
What possible reason could you have for wanting to hide the fact that you have a Facebook account? Why so paranoid?
In any case, all you need to do is tweak your privacy settings and the most anyone outside your friends list will see is your name and picture (if you've chosen to upload one). That's all. Storm in a teacup.
To say it's OK is akin to being forced to stand in a room with people you were trying to avoid but being told, "it's OK, you don't have to say anything to them."
No, it's nothing like that at all. You're not in the same room as them; you're outside the house, with only your face and a nametag on display. They can't contact you or check any of your personal details.
If you don't want people to find out you're on Facebook, there's a simple solution: get off Facebook.