Is front-running allowed under PFOF?

I’m reading this introduction to PFOF.

https://centerpointsecurities.com/payment-for-order-flow-guide/

It claims that those buying flow are allowed to front-run that flow. For example, if a customer sends a buy order to $3 and the current best offer is $2.99, the HFT firm is allowed to buy in the lit market at $2.99 and then fill the customer at $3.

Is that legal? I thought that the HFT firm was required to give better-or-same as the current best offer?