There is a disconnect here that needs to be clarified but you are actually part correct. The 'corporation' owns the shares, but shareholder 1 owns the corporation and thus it is his now. Shareholder 1 now owns 100% of the company but the company is worth 50% less because it spent half it's money on buybacks. So shareholder 1's value of ownership did not increase at all, only shareholder 1's % of ownership. Stock buybacks do not add value to a company and are not like a dividend at all. All they are is an indicator that the board thinks the shares are undervalued.
So...I know realistically, this isn't possible, but what if a corporation bought back every share except for one. Would that one lucky shareholder who probably bought his one share for $20 now own the entire corporation?