i'd consider it an internet event if it happened on the internet, not spread by the internet. truthfully, almost everything we know now comes from the internet, from medical advice to theological truths. so with that in mind, everything happened on the internet.
however, if you think about rebecca black, psy and even justin bieber, they happened because of the internet, as in, if it weren't for the internet we still wouldn't know who they were. memes, rage guy comics, viral videos, etc are what i'd consider internet phenomena. everything else was just news that spread on the internet. i'd classify the cupcake thing to have happened on the internet too, but definitely not the olympics.