We’ve repeatedly asked the seller to provide the tenant’s rental payment history, but there has been no response.I asked my realtor how we can verify the payment history, but she didn’t directly answer and simply mentioned that I can either accept or deny the lease (it’s a month-to-month lease, which I’m fine with).Should I move forward with the sale?

Assuming your offer got accepted, the owner would need to get a unit vacated by closing (obviously this will need to be communicated).

It's a real pain to enforce but it's worth it.The majority of carriers right now have a loss rule on new business that varies but goes something like this... they will not accept your new policy if you have a loss in the last 3 or 5 years.

Maybe Vrbo is doing more a/b testing.

If you told a seller, on an accepted deal.

Meanwhile, they form LLC's in preparation for when claims or conflict will arise almost as if there is an acceptance this will occur. 

Any help is accepted and I am definitely willing to hear your advice! 

One of my major screening criteria is you must have the deposit and first month's rent plus pet deposit within 48 hours of acceptance. 

Does the request pass the sniff test? 

If you are paying a fee for every property you make an offer on you are offering way too much...you should be making your offfers low enough (MLS) that only1 in 20-30 will be accepted.