Is it possible for someone to license something that is not copyrightable (e.g. too trivial, or no creative work), and is the licensee bound by that license if they use the "licensed" version instead of the free one?
This is a bit hard to think about, but suppose there are two ways to start using such work. One is to simply make a copy and use it, since it is not copyrighted. The other is to license it from someone (who may be allowed to license it, it's his work as much as anyone else's) and possibly be bound by the license (since you chose the second way, using a licensed version instead of the "free" one). Of course, both versions of, let's say, a digital work would have the same bits, but they might have different rights because of their different histories of how you got to use them.
Would it be possible to license at all? If so, would the licensee be bound by the license if he or she took the license route instead of the route of getting the work without a license because there is no copyright to oppose it?
I think it might be a bit like contract law, that if you accepted the license agreement (you didn't have to accept it, but you did, so you're bound by it), you might have the obligations of the (license) agreement. The question is whether you can "automatically" switch from the contracted version to the rights-free version, or whether you're bound once you've accepted a superfluous license.
A concrete example: The current interpretation seems to be that there can be no copyright on neural network weights because they are not a creative work. Nevertheless, companies and many people who create derivatives put licenses on their weights, claiming that downloaders must respect the license to use the weights. Many even ignore the upstream license and attach a new license to their weights.
In addition to the general question of whether they can impose a license on a work that is (currently) not copyrightable, things get complicated because re-training almost always changes all the weights in the file, even if the results the neural network produces may be quite similar.