OK, on a serious note, I often play while "in hiding", meaning that it game settings I use the "offline" setting. At the same time, I usually have the webpage open which shows my status as green (available). There have been times when I am playing like this that I get an invite from a friend, even though I am in hiding. I asked him how he knew I was online, he didn't, he just typed my name in the search window when inviting.
Other times, I get random invites from people I do not know (which I do not accept). I have no idea how they even know I exist when we have never played, not in same club and I am in hiding. I can only presume, somehow they come upon my online page, see I am available and type my name in the search window when inviting.
Another thing I have noticed, sometimes when I look at my friends list, on the game pages (not the website) there is a grey box (Play Button) as opposed to green. Does grey mean you are online but busy? Is my box grey when I am in hiding? I imagine if my box is grey, when in hiding, friends would still know I am online. However, if this was the case, I would probably get a lot more invites from friends when in hiding. As of now, the only friend that invites me to games, while I am in hiding, is the one who manually types my name.
So, I have to assume, other than be lucky and randomly tying the name of someone who is hiding, the only way to know if they are online is to check the webpage profile.