> 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.
If you are having trouble understanding, just ask. Of course I'm talking about a websites terms of use.
As I understand it, terms of use on a publicly accessible page aren't enforceable. That's why it's legal to e.g. scrape pages of news sites regardless of any terms of use. If it's curlable, it's fair game (but it's fair for the site to try to block my scraping).