Long story short, I was told that my Skype account is online even when I am totally sure it is not. Couple monthes I was living with that issue, while I've got some time to make an investigation
According to Skype forums this issues appeared with introdution of "cloud chats" (and new client apps, when all old clients "were banned"). Cloud chats from some clients by some means "keep your online status". In my case it was a online sessions from my Android Skype client.
Go in chat with anyone (doesn't matter who) and type this command:
(it this shows all your current "online" session, for me it was 3 of them !)
If you see more than one session there, then type
it will logout all sessions except current one.