Utilizing her renters insurance (if she has it) to cover the claim will require going against her liability and that will require the insurance company to investigate, which will take a long time. 

And since I don't have any existing relationships, I have to start fresh with someone. 

I would suggest investigating how to get additional funding for a local purchase and do the BRRRR where you can keep a close eye on everything.  

I would investigate further as to what is going on. 

A few weeks after closing I was at the house working and a private investigator stopped by looking for the previous owner.

I would wait until the home is freshly cleaned and painted to show it.  

I do love the idea that they could be investigated for taking advantage of sellers while at the same time everyone says they are overpaying.

I've been investigating in Setúbal, Portugal for the last 3 years on buy to let but looking to scale in the next years.

Investigate and use as a learning experience, then come back and share your findings👍

Personally, I wouldn't play any of those games-- you aren't an investigator, and don't play that-- either decide to rent to her, or not-- and stand firm.