They don't "insert" themselves, they were there before you came along. Your market order trades with them because their price is the best one currently displayed. As for an HFT firm "seeing" your order and front-running--you're just making stuff up.
Flash Boys is an entertaining write-up of how the firms are inserting themselves, and how they are "seeing" orders at one exchange before the order arrives at another exchange.
The "Flash Boys" case is a funny one. The HFTs did see the orders--but so did EVERYONE else, and in basically the same instant, because all transactions are publicly disseminated. Your point is right in a very narrow sense and very wrong on every axis that actually matters.
I'm mystified as to why Flash Boys didn't valorize high-frequency trading. It's a Moneyball story where the scrappy nerds use computers and math to out-compete the dinosaurs. Oh well.