This one still bugs me, so I'm still thinking.
Landlord says its not creosote. OK, for now, I'll assume that is true. So, what else can it be?
You mentioned that a wood stove "used to" sit in that area. Which means there isn't one there now, right?
So, why would you have a wood stove, and then take it out? (thinking out loud).
Maybe... the wood stove had a problem, and there was a fire? that they managed to put out before the whole place went up in smoke?
IF SO... it could be charcoal, not creosote. (from the sub-floor burning)
Cleaning the carpet with anything wet will still make it a problem.
What happens if you work some baking soda, or corn starch, into a small bit of the stain, and let it set overnight, and then vacuum? Can we absorb this stuff?
Just wondering...