Float test is not a reliable indicator of seed viability. Some species that grow close to water have developed floating seeds to aid in spreading their genes further afield.
Sometimes the kernel may not have completely filled the shell, even though it is fully viable, leaving some extra air inside that may cause the seeds to float.
While not relevant to fresh collected seed, I have noticed that stored seed seems to float more than fresh seed. I'm guessing the embryo inside starts to dry and shrink, sometimes enough to change the seed from sinker to floater.
In the case of that hornbeam, do you know why the leaves were dropping early? Early leaf drop would usually indicate some stress or even death of the tree. The tree may not have had enough spare energy to complete the seed development. I would not put a lot of trust in seed from a tree that's not fully healthy.