Yes, sometimes video websites will block an iMovie song because of copyright, or alleged copyright. The iMovie license gives you the right to use the song, royalty free, in your projects, for personal and non-commercial use. However, "royalty free" does not necessarily mean copyright free. The iMovie license states that you should consult an attorney if you have questions about your legal rights under the license agreement. Also, iMovie has a "legal" website where you might be able to get an answer. Here's the link:
Legal - Contact Us - Apple
Facebook may have some some procedure for disputing the claim and you could try that. You could argue that the iMovie license gives you the right to use the song for non-commercial purposes.
Otherwise, you may have to substitute a new song that will pass the copyright filter. It could be your own composed song, or a song from one of the websites on the internet where you can purchase royalty-copyright free songs. I think some of the websites offer them for free.
-- Rich