Finally saw an episode of Ghost Adventures. I had honestly never seen it before; I don't watch many of those programs. It'd be like a cop going home and watching cop shows.
I got a bit frustrated with it because the history they told was flat-out wrong in the beginning. The remains of Jean LaLime were not burned up in the great Chicago Fire. The bones though to be his were presented to the historical society as a gift (I'm sure they were just thrilled) when they were unearthed during construction, but not until the 1890s, some twenty years AFTER the fire. The Historical Society still has them, as a matter of fact. We covered this in a post nearly four years ago. They aren't 100% sure that the bones are really LaLime's, though, and keep them in storage. Eventually they may decide that they should be re-buried under the Native American Grave Repatriation Act.
Kinzie was, in fact, acquitted of the murder of Jean LaLime on the grounds that it was self defense, but I've never really bought that. The story went that Kinzie stabbed LaLime only after LaLime shot him in the shoulder. Some believe this, some don't.
I'm not sure about the story about women seeking shelter in the building that stood on the spot during the fire - much is made in historical accounts of the society losing 60,000 books in the fire, but I can't find any contemporary references to women dying there. Running into it for shelter during a fire would have been an odd choice, it seems to me, but I'll withhold judgement until I've looked into it further.