Is it possible that Apple Music is somehow involved in the purchase chain? Songs from Apple Music are all DRM (Digital Rights Management) protected. The DRM protection remains even if the songs are subsequently downloaded to iTunes. DRM protected songs cannot be used in iMovie. In the event that that is your situation your solution would be to purchase the song directly from iTunes without involving Apple Music in the chain of purchase.
If the above is not your situation, usually songs purchased directly from iTunes after year 2009 are DRM free, but not necessarily all of them. So it could be that the particular songs that you purchased carry DRM protection. In that event, iTunes has a "Match" subscription program for about $24.99 per year whereby you can download DRM free matches of your DRM protected songs. I am not sure that this would work if the songs originated from Apple Music. You can get more info about the Match program from the iTunes website.
-- Rich