That's where the "follow the same rules expected of the PPD" comes in. And of course there would be rules and regulations for whatever equipment a Hero uses, but those would be covered under their own laws. Also, the most punishment I've seen in-lore for a bad failure is in an Indigo mish, where Malta attempted ruin a Hero's career by blowing up a building, where I assumed the Hero would either just have their license revoked, or contacts simply wouldn't talk to them. Nothing ever pointed to anything close to "dereliction of duty", and the new Atlas arcs point out that there are Heroes who "hung up the cape", so to speak. Can the FBSA command them to do a task, as well? It also doesn't take into account alien Heroes from other planets or dimensions, volunteering their services.
Edit: Also, to be clear, I'm talking about Heroes who try their best to follow the rules. Now, for the Vigilante who decided to enganger lives by leaving the disease factory to go after the bad guy? Yeah, I can see the FBSA getting pissed and pressing endangerment charges. A Hero that, for whatever reason, came up short and likely nearly lost their own life in the process? Sorry, but "dereliction of duty" and being ordered around, I see as going too far.