> why should they not be able to choose "not for training uses" even if they put it up publically?

I'm having trouble even parsing that question; "Publically" means that you put yourself out there, no? It sounds to me like that Barbra Streisand thing of building an ostentatious mansion and expecting no one to post photos of it.

I suppose you could try to publish things behind some sort of EULA, but that's expressly not public.