HFT firms perform a different kind of front running. If I'm an HFT firm and I see a large buy order on the books at exchange A, I can use my low-latency links to exchanges B, C to execute my own buy orders there before the rest of the market reacts.
It's not illegal, but it is still front-running the rest of the market due to latency arbitrage. Check out Flash Boys by Michael Lewis for more on the topic.