I absolutely despise this public dungeon! On every DC character I've made, I waste over an hour trying to get the dirt tossed on the flames. I've /bug reported it numerous times, log out/in dozens of times, zone out/in dozens of times, dropped the quest and picked it back up numerous times, teleported to guild members who are in a working instance of the dungeon, etc.
(Searching for "bad man quest" only really returned this thread, so I'm posting here instead of creating something new.)
I had this same problem last night, did exactly the same thing you did with no luck, but finally out of desperation I used /stuck. This killed me and placed me back at the wayshrine at the entrance to the Hallows and I was able to then extinguish the fire and continue normally.
Confirmed, using /stuck and respawning at the front does allow you to throw dirt on the fire. Glad I found this thread, I was starting to get pretty irritated about this bug.