I'm sympathetic to your point, but I'm sure there are heightened trust levels between the participating orgs and confidentiality agreements out the wazoo.

How does public Claude know you have "full authorization" against your own infra? That you're using the tools on your own infra? Unless they produce a front-end that does package signing and detects you own the code you're evaluating.

What has it stopped you from doing?

You can do pretty much anything you want with public claude if you self-report to it that you have been properly authorized.