Unfortunately they will have to pay Yoko. You see the fair use rule doesn’t apply. This is a for-profit movie. The copy right rules are clear. They know it too. That’s why the licenced the other songs. They also stole graphics.
An TV news programs aren't? I don't think the fair use doctrine distinguishes between profit and non-profits; and it is a documentary film. Can you show the law that says a for-profit cannot assert a fair-use defense?
Besides, you said it wouldn't make a profit.