You aren't invisible!
I already posted this earlier in Skype Journal with the title How to make an invisible person visible with a Webcam, but the bug persists. Today i noticed that a new friend appeared offline with a webcam. When you really are offline, Skype does not send the "webcam symbol". Here, it was shown, so i knew he was online! This is clearly not how it should be. TO BE CORRECTED!
To avoid this, you should tick the radio button "Show that i have video to no one" in the Video Options of your Skype client.
Another trick without a webcam:
when you see that a person is offline: send him/her a chat message, and if it doesn't provide a message back that it hasn't been delivered yet, you know the person is online. You can even see if the person reads your message: there is a faint glowing up of the avatar (picture) of your contact in your chat window if he opens his chat window!