That's literally not how buyouts work. The public stock price is certainly one factor of many that go into calculating the acquisition price, but it is not an absolute floor. One counter-example that comes to mind is Yahoo!, which was purchased by Verizon for less than its market cap at the time.
It’s not an absolute floor no, but it’s a strong factor in price determination. It feeds back the other way too, if a competitor is acquired for far less than public price it smacks the public price of competitors.
