I have no idea why the answer to this problem is "using Basecamp!" - That doesn't make sense to me at all. For me the answer has been to turn off notifications and shut Slack when I need to go heads down, but review it multiple times a day and chime in where needed. It's still such a vast improvement over an email or email+issues based workflow.
The CEO of a flat company probably has a need to see everything, JIC. Not all use cases are equal.
And Slack does an excellent job at demonstrating why that is idealistic nonsense and simply bad management that doesn't work, simply by making it possible to actually see almost _everything_.
It's one of the great things about Slack, it's much like Scrum in that respect: it may not be the answer, but it sure as hell will confront you with what the actual questions are.
Unfortunately, people who don't want to face their problems will immediately turn around and blame the tool/method. So very typical.