Plus there are two different issues.

The composition itself might be in the public domain, but the *recording* of the composition is almost never in the public domain unless (a) it's an Edison cylinder recording produced in the late 1800s, and therefore expired from copyright (b) the copyright wasn't renewed when the copyright laws required that, or (c) the artist(s) that made the recording dedicated it to the public domain.

It's worth noting that if I record somebody else's (non-public domain) tune on a CD I sell, there's a compulsory license fee I can pay to the composer that will, when paid, automatically enable me to use the song. However, if my same recording of someone else's song is captured on *video*, then there's no compulsory license and I have to individually negotiate a "sync license" with the composer's representative.

For many years, "happy birthday" was thought to be in the public domain, but it is not, and now the descendants of the two women who wrote it make a tidy sum of money each year from the use of that song in movies and television, and they also collected a *lot* of money for infringing uses of the "public domain" song. (That's also why most chain restaurants don't sing "Happy Birthday" to their patrons with birthdays.)

Long and short: The use of royalty free music that you've actually read the license and been clear that it allows your particular use is a good idea. The use of music that's supposed to be in the public domain, as Basschick said, is a lot more iffy.