Your first statement is not true, at least in the US. Copyright gives the holder the rights over the ability "to perform the copyrighted work publicly" (directly from US law). The wording from the law on public performances: "to perform or display it at a place open to the public or at any place where a substantial number of persons outside of a normal circle of a family and its social acquaintances is gathered". Even in the strictest interpretation of the law, no reasonable judge/lawyer would find that singing to a single friend would meet this criteria. So someone can absolutely sing a copyrighted song to a friend without being in violation of copyright law. You can even do so with a group of friends (as long as it is what is deemed a normal circle of family/friends).