For instance, if I take a copy of $BIG_BUDGET_MOVIE, and resample the video frames from 1080p to 720p through a purely mechanical transformation, that doesn't make the output public domain.
The BSD license doesn’t explicitly convey the right to create derivative works but it does convey the right to “modify” the software. (They seem similar but “modify” is a narrower verb.) So is this a modification? A derivative work? A new work entirely? If it shares no code with the work from which it was derived, things are more complex than it may seem (and it no longer fits the “compressed video” analogy very well).
Surely you wouldn’t say a Spanish translation of a Harry Potter work is in the public domain while the original work is under copyright?
I imagine a court would call it a derivative work if tested.
The licenses tend to say unmodified or modified copies can be redistributed in source or binary form “provided that the following conditions are met”. Relicensing the code in a way that guarantees those conditions are met has been the accepted thing to do in the community for years - whether that’s GPL/LGPL/AGPL or a proprietary license.
As you said, the question has never been litigated or settled.