I believe that's their primary business model.Seems like this would be a great bonus! 

We sold our (primary) home recently.

If the tenant has a reasonable explanation and a solid plan on how to recover we will work with them.You are asking the right question: how are you planning to pay double rent next month?

Income taxes- if needed can you use your 2 year primary residence deduction if a taxable event occurs.13.  1031-  if any part of the insurance claim is a taxable event is there some way to do a 1031 with lenient time frame adjustments?  

It is an investment property, and does not meet the qualifications of being her/their primary. 

Like you said , anyone can check the history,  I do have cameras installed and I do check twice weekly, it's not too far from my primary home . im a first time investor, is it ok to DM the listing to see if I'm missing something?  

Reason why is because FDIC Bankers "Do Not" charge points on traditional programs like primary homes, standard investment purchase and refinance, Second home/vacation homes.Lenders, Brokers all charge points to meet their Loan officer compensation plan (commission).

I have found that I get more appreciation on the single family house because I can sell it to an investor or as a primary residence.

What if the primary applicant moves out with no notice?

Clearly, they failed in their primary responsibility to you as their layer of due diligence was a mere gossamer like patina.