That's fair. We're not going to get an official answer whether it replaces the normal Burn rules or is in addition to them, because it isn't supposed to matter. Again, I recommend playing with the rule that Burns deal Flame damage, because they're supposed to and will receive an update to that effect in the near future.
Don't all flame conditions automatically deal flame damage by association? Similar to poison conditions always dealing poison damage. It seems the distinction of direct or critical damage is separate from the damage type association.
Where are you getting this "association" from? It's just like with spells like Ghoul Rot. It may have had the Poison subtype, but it had to receive errata before it actually dealt Poison damage. Conditions can also have a subtype without actually dealing that type of damage.
I don't think the Ghoul Rot example is comparing apples to apples. It is a spell and spells have subtypes. The spell effect did not have any association with a poison condition or damage type without the errata. This is because direct damage is not associated with a damage type. That is why the errata was necessary. However, some conditions are defined in the Codex as associated with a damage type. Therefore, any effect or damage caused by these conditions would, by casual relationship, be associated with the damage type that created the condition.
I don't see anything in the rules that give conditions 'subtypes', but perhaps I missed it. Perhaps we need to add subtype as a Codex term to make this clear as to intent.