This is the heart of the problem with IEX's explanation of the markets, and why I think most people view HFT as unfair. But its not how cross exchange market making actually works. The HFTs are not rushing to buy up existing inventory from others who are selling it, in an attempt to screw others. They are the ones who are originally offering to sell it in the first place. They aren't rushing to buy, they are rushing to change the price of their inventory.
The metaphor I like to use is that of a chain of gas stations running down a highway, owned by the same people. If a tanker truck pulls up at the first two and buys up all their gasoline, it would be perfectly reasonable for those first 2 to call ahead to the rest down the highway and tell them to raise their prices, as they clearly were being used to supply someone else's industry at lower prices than they should.
That phone call is what IEX prevents, so that their customers (guys with big tanker trucks) can buy gas without impacting the price of gasoline.