The reason we want a private forum is to weed out all the theorycrafting that goes on when people who have numbers are posting feedback in front of people who do not have numbers. This is one of the primary reasons why the old TR failed -- there was no way to determine who was giving real feedback, and who was extrapolating based on other people's feedback against existing champions. There were even a couple of champions released very OP or UP because of theorycrafted feedback that was not based on actual gameplay.
It also led to another primary reason why the old TR failed -- information leaks. The TR was patched 1 week ahead of live. As such, it contained most of the content rolling out in the live patch the following week -- sometimes even things that were not going to be released at that time. Some people who had obtained TR access by way of a dropped link (like what you left out in the open I'm assuming...) started posting TR changes onto different websites, spreading the information all over the place for anyone to find, and then flood GD with complaint threads about. You know how the whole "You're nerfing Irelia AGAIN?!?!??!" meme started? Because of information leaks from the TR by people who had not been invited to join, but who had "stolen" their access.
Furthermore, because the forum was not private, patch notes could not be posted regarding the TR, making it extremely difficult to test any changes made to existing content -- the only things anyone could test and know they were testing were the upcoming champion, and any new items that were under development. Anything else, buffs or nerfs, was largely missed simply because no one knew what they were.
Do also keep in mind that "Public" can also fit the definition of "outside the company". TR access is a privilege, not a right. Riot could easily revoke it from any of us at any time (and I suspect several of those "I'm banned... but invited to the PBE?" people will be losing theirs, but I don't work at Riot so I don't know).
Creating a private forum, or at the very least a forum that is read-only for not PBE members, will greatly enhance the quality of the feedback that comes from it, and ensure that it actually IS feedback, and not theorycrafting.
Limited number of people and closed access to the PBE forums, not because the patch notes won't get out, because that is fine... but mostly to create the right environment for constructive discussion. Let the GD remain the GD... but it shouldn't spread to here.