Can an HFT Firm Be Accused of Front-Running, and under What Circumstances?

Yes, an HFT firm can be accused of front-running if they gain access to non-public order information. This could happen if an HFT firm is affiliated with an exchange or broker and misuses that privileged data, or if they engage in activities like "latency arbitrage" that cross the line into using internal, non-public system information.

Simply being fast and using public data does not constitute front-running.