A lawyer or copyright expert can correct me if I'm wrong, but a sufficiently novel use of public work, or fair use of private work, can be copyrighted. So the original source material doesn't belong to the King estate, but its use in the context of the speech does.
If I make a collage of other people's works, the other works still belong to them, but the way I put them together belongs to me. Actually, this doesn't seem terribly "nuanced".
I think the point being made was that you can only do this if the owners of those works let you (or you intend to claim fair use). If they had been required to license all works that were incorporated, that would likely have severely changed the speech, so the fact that it is what it is is largely due to the fact that they were able to lift all that material. Yet that same opportunity is now being denied others.
Indeed the copyright status of derivative works is somewhat controversial. Perhaps one of the most famous examples of the issue is The Grey Album by Danger Mouse (2004) which heavily sampled both The Beatles and Jay-Z. EMI was very keen on stopping the distribution of the (then) unknown, underground album, however they have given up eventually after facing widespread public outrage.
If I make a collage of other people's works, the other works still belong to them, but the way I put them together belongs to me. Actually, this doesn't seem terribly "nuanced".