She sounds like a complete fruit loop!

Maybe things work differently for Americans than elsewhere. But, every time I rent somewhere new, someone - either the landlord or an agent - does a quick tour of the place with a checklist. They show me what is in the apartment, I sign off, indicating that I am liable only for damages exceeding normal wear-and-tear. If I don't want something, I might ask the landlord/agent to remove it so I can replace it with one of mine, and everything is agreed upon and signed, so that we all agree who owns what, and what items I am responsible for removing at the end of my tenancy. Very little is left to "he said, she said."

I don't even know why she launched straight into her sales pitch on initially meeting you, seeing that she wants someone to take her place "by the end of June" so she doesn't have to pay double rent. If I wanted to be out, the last thing I'd do is come up with some unconventional and inconvenient suggestion that could discourage someone from taking up the place.

And lying about ownership of the dishwasher when that could easily be verified by talking with the landlord? I think she has some issues.

I understand this situation was not ideal seeing the urgency you faced in securing a place to stay. But, whenever I want to negotiate something, I want to deal with only one party if possible - either the previous tenant or the landlord, not both. Better the landlord than the previous tenant. This kind of "he said, she said" back-and-forth often leads to unnecessary drama.