You're all talking past each other. "Taking a company private" has nothing to do with stock buybacks. Stock buybacks are when the company itself buys its own stock and then cancels the shares, which increases the percentage ownership stake of the remaining stockholders. Taking a company private means that a single large investor (or a cooperating group thereof) buys 100% of the shares and then votes to delist the company from the stock exchange and stop trading the shares publicly.