I think that's conversation come up when Akihito find the secret room and it's just casual talk, not something so serious.
I could be mistaken but there are some things happening in the actual manga that I have seen written in various fanfiction. It's possible that she is getting her inspiration from fanfics which I think is pretty cool.
I never thought it would be serious, but think of the time Akihito figured out that Asami killed that stalker guy who touched him, Asami never blatantly admitted to it (only not so subtly alluded to it), not to mention, talk of Asami's business or acts of killing are kind of a touchy subject with them. Then again it also never explicitly stated that Asami killed the former owner (I felt that it implied that but I could be wrong, especially with how easily Akihito brought it up in this chapter).
So yeah, I simply wondered when they would have bothered talking about the previous owner because I doubt Akihito would have asked about that unless he had a reason to.
I have to but it's usually something very generic that could easily happen in this kind of series, so it's usually a coincidence. I've never seen a conversation like that in one though.
Thanks for the update. Somewhat offhand thought but I found it interesting when Akihito mentioned the previous owner dying there at some point, meaning that Asami must have told him about that at some point. I wonder how that conversation came up and just how much Asami told him about it.