Theres a good chance it had to be a private room because they were taking the chance of being seen. Kash is not an unknown person - he is recognizable. If he is recognizable, people will take notice of who is with him. And this board is not unknown so there couldve been a chance that someone familiar with this board saw them.
It had to be a private location given Kash's background in intelligence unless they WANT people to start putting the pieces together for a Q reveal.