The same assumptions are true about giving any human that shareable link. They could pass it on to anyone, screenshot it, paste it into their own session. This has been true since before "share with link" permissions on Docs and elsewhere.

If you click "provide a shareable link" you should decide (and behave) as though that made it public.

I'm not saying it's good privacy posture on the side of the companies, but how else do you think that would work if there isn't any authentication step for the person viewing it? Even with authentication, "three may keep a secret, if two of them are dead."

Chat UIs are a minefield of “if you accidentally click this your data will be shared or trained without you realizing it!”