I am a composer of free creative commons music which luckily, has not been claimed yet but, I am in the business since 2007 and know one or two things about ContentID, copyright infringement, and why music triggers copyright claims. If you ever receive a copyright claim that has not been issued by the copyright holder dispute the claim; as previously noted in this thread, but ALSO make sure that the composer/copyright holder is being informed. There are steps that can be taken against false claims and since money is involved, publishers, music aggregators and distribution platforms will take any information about false claims very seriously. Sometimes even composers infringe copyrights if they do not compose their music from scratch, note by note, and/or happen to use pre-produced loops within their production - in that case, there may not be much that can be done. That's also why it is important to check the source of the music, make sure it in fact is "copyright free" before potentially running into these issues.
Here is what you can do to minimize your risk:
1. Pull the music into your video editing program, attach a simple picture to the music, render the video and upload it to YouTube (some even have dedicated accounts for doing this) just to see if it already triggers any copyright claims before you spend endless hours in editing.
2. Only use music that you are allowed to use, don't trust the words "copyright free" blindly and don't get it from a shady source, no matter how good the music may be.
3. Try to find additional information about the composer, it is always a good idea to know where the music comes from - if there are any questions or issues, you will know who to contact. Any serious composer has social media accounts or a website these days - can't find it? Skip to the next track.
Last but not least, don't be silent - if you notice something out of the ordinary make sure to inform the people involved - ContentID is still pretty primitive and can be "tricked" (panning, changing key/speed, .etc) the fight against false claims only works with your help.
Hope this helps!