When inviting users to a project, the 'quick list based on other work projects' is bad

[prioux]

When inviting users, we get a huge panel with checkboxes for all users; at the bottom a utility panel with other projects are listed, and this panel seems to include 'public' projects, which makes no sense. They should not be shown there.

This form has always been horrible, and we should consider changing it to be more like the NH interface version. But before even doing that, I just want the public projects not to be available. Also the controller code should validate these values too.