VT - in theory, yes, we can all be "done" for not paying a copyright fee when we sing a song "in public". I remember in my jazz days, playing in hotels, that the hotel manager would often bring a PRS form in for us to fill in with the titles of all the songs we'd performed for the dance - so that the hotel could pay, by the way - not us. We used to make them up - couldn't be bothered to fill them in properly.

However, the reality is slightly different from your scenario. There's a significant difference in posting your own version of a song on YouTube and you actually posting someone else's performance without their permission - particularly if you post a commercial clip which could reasonably expect to be sold and make money. The law is an ass sometimes, but not that much of an ass!