Apple Music as you point out is a subscription service, as such you do not own the tracks. You are only renting therm, and have access to them while the subscription is active. Just like you don't own the gym equipment when you sign up to a gym. you can use the equipment and their services only while you are subscribed and can't take the gym equipment home with you.
Same premise with the Apple Music subscription service. All subscriptions services work like this, because music labels want to prevent piracy of their music.
Adding them to a movie you are making would in essence bypass the subscription and allow you to keep them even if the subscription was cancelled which is obviously not something the labels would allow.
If you want to use music in a iMove you need to actually purchase the songs from the iTunes Store.