I would say that it would be very strange if the copyright strike for the piece in Youtube's Audio Library was legitimate...I would actually think that that strike is false (and should be challenged).
If a piece of music is truly in creative commons (you really shouldn't talk about things not having copyright...rather, it's more precise to say that the copyright owner is using their copyright privileges to put a creative commons license or is practicing copyleft), then I would think that there's more to the story. Often times what may happen for example is that a particular piece is in creative commons, it gets used in another work that is not in creative commons, and the latter work tries to strike people for using the former. This shouldn't happen, and this should be challenged, but it's still a hassle.
Or, with public domain pieces, what often happens is that the work itself is in the public domain, but there are still recordings that are copyright protected, so there may be a content match when you're not using that particular recording (in which case, you should challenge that) or there may be a content match if you're using that particular recording (in which case, you really are in violation of copyright...even if a composition is in public domain, a particular *recording* of that composition might not be)
I think that Surreal469 raises an interesting point. Sometimes, you will have "royalty free" songs. These songs just mean that you don't have to pay an ongoing license fee (that is, the royalty) to use the song. But royalty free songs usually come with an upfront cost.
If you want truly creative commons music, you can't just go with royalty free...
Neimers also raises a good point. Even for creative commons, there's lots of licensing schemes. Many people will require attribution at the very least, so you don't want to get in trouble just because you didn't comply with the terms of the CC license.
