Yes, you wouldn't be able to use it w/o permission. Sure, people use music for Youtube, but what you don't notice is how many vids get pulled once the copyright owners contact them. Youtube itself doesn't police its site; it relies on the "honor system" that posters understand copyright law and will abide. They will pull violating vids if they are contacted by copyright holders, but as you can imagine, it's not a very effective guard against infringement. This is quite an issue with artists like Prince, et al.
I'm sure you wouldn't want to get on the wrong side of the Sinatra estate. :P
Personally, I hate being accosted by music when I visit a site. Often, I have my own stuff playing or I'm trying to "surf quiet" to let others sleep.