When you purchase royalty-free music, you are paying to use that material (usually with some stipulations, like, you may use it e.g. broadcast, internet, etc., but can’t resell the collection). Just because someone buys a finished project from you doesn’t automatically entitle them to use of the assets- if that were the case, you would ‘lose’ control of your own video everytime you sell a DVD or someone views your work online.
It’s easiest to think of it not as ‘owning’ the music, but having a license to use it. Unless it’s under Creative Commons, songs require acquiring the license from each and every user to keep it above board. HTH.
