I don't recall mine having a light. It definitely wasn't my cousin. It may have been something malicious I installed without knowing. Maybe I downloaded and installed something from Kazaa or whatever the current P2P file sharing network at the time. I thought it was weird that it happened right after I exited Diablo 2 though.
The most common way to get infected is running infected applications.
As for your webcam, did it not have a light when on?
Also, very likely it was your cousin or someone you know.