Weather or not my logic is "flaw" is an irrelevancy, since we can just look at the relevant law. You MAY qualify for fair use when you use a song in a video you make, but you also might not, and the fact that you are not intending to make money off of this video is not the sole deciding factor. In fact, there is no single objective deciding factor as to what constitutes fair use and what is infringement, which means that you can get sued and may have to argue your case to a judge. If you post an edit on youtube that gets a lot of views (say the hundreds of thousands), then it could be argued by the copyright holder that your action is depriving them of revenue, even if you're not making money off it. Also, since Youtube has adds on their website, they ARE making money off of it, which is why they have a policy of removing copy written material when they become aware of it. If they didn't do this, they would be sued (and have been).