False.
HFTs and other trading firms actually buy up the order flow from brokerages. In fact, retail investors making trades in their brokerage accounts are actually referred to as "dumb flow". Having access to the order flow and controlling the routing of it can allow them to jump in front of your trade.
For example, they could see that your limit order of $1134 came in when the lowest ask price was $1133.90. They could buy that for $1133.90 and sell it back to you at $1134 for a 10 cent profit.
It's not too much different than in the old days when the market makers would delay buy/sells calls to their pits to their own advantage in order to scrape a small profit on the spread.