let's assume you are right. Also assume that the two people in the dark room are both somewhat rational investors. Then let's imagine that they are trading at a price that is significantly different than the open price. Why are they both OK with that price? If the price is higher, the buyer could be buying for less in public. If it's lower, the seller is the one that could sell in public for a profit. So one of the two sides is making an obviously bad decision.

The idea instead is that in a dark room, you can trade large amounts of shares without HFT interference. They'll probably be trading pretty much at the public price, just without sending all kinds of information about the fact that they traded into the world.