He reached out to the insurance company he uses to insure all of his other properties and he was just outright denied. 

You can deny a large family for example with a 2bdr unit or a 1 bdr unit as there is a bedroom and sq ft requirement to be met per person and for minors of different sexes.A studio can be limited to two or two and an infant as that meets the one bedroom requirement.Saying they must be single or limiting to one person is discrimination as to family composition, you can't define what their "family" can or can not be.

He did it without debt, you cannot deny that. 

You might be able to use annual statement + transaction history from Dec 30th to present to make it work.If the funds cannot be sourced adequately, what often happens (as a sort of compromise alternative to "loan denied") is that the will pretend they never saw the money and subtract that amount from your current balances.

I've had clients with home warranties that cover HVAC, however, if the coils are found to be rusted or dirty sometimes they will deny the claim due to lack of maintenance.

The claim will get forwarded to the Police Department to get investigated.The Police Deparment will either approve the claim or deny it.  

The seller still denies everything.I wrote pretty much my last letter, making my case, and because of the new year weekend, dont expect a response until next week.So, thats what this post is about, what do I do now ?

Is it ok for me to take the application and then wait a day and deny it due to the past evictions and then send an adverse action letter?

If they dont approve it, do they come back with a request that I would need to make X,Y,Z changes or is it an all out denied and that's it?

I decided to stick to my criteria and deny her.