But why is the broker giving a fee to Robinhood to handle the trade? That only makes sense for them to do if they have the stock available at a lower price point than the Robinhood user is getting--had the order gone straight to market it would have cleared at a better price.
The broker is paying Robinhood for the burden of handling the order. Why? What's the profit for them? If they just sent your order to the market and it cleared at the market rate, there is none. Instead they do a number of tricks that are designed to profit off of foreknowledge of the order before it hits the market, while trying not to run afoul of front-running regulations. When they succeed, they do so by taking money that you left on the table.
All that said, I still use Robinhood. I don't trade at high enough volumes to get upset over these hidden costs, and I'm under no illusions that other retail brokerages aren't doing exactly the same thing.
I'm skeptical that this interpretation/loophole actually exists. If you're executing the trade, you're the broker. Shuffling it between firms doesn't absolve you of the responsibility. The fact they got fined means it clearly didn't work.