Most likely the point that the agent was trying to make is that there is an abundance of buyers who are paying cash under $100k and the chances of your financed offer being accepted are significantly lower if the seller is sitting on a pile of cash offers. 

What is the first thing that happens when I get an offer accepted?  

The title person contacted me before the banks closed, to let me know they don't accept cashier's checks for more than $50k.

Strong screening process with solid qualifications will allow for a landlord to find another reason to not accept them.  

So rent might go up 2% to 3% a year but they want to pay a rent bump of 6% in 3 years etc.National tenants there is generally less risk in accepting these terms as they are likely to still be around and you see the increases.

I absolutely do not accept any evictions, and the renter has to make 3x the rent for me to be comfortable...

Not sure what the bank would accept for the house.  

If I shop around to other banks, is it possible that I can find one that will accept me?

The accepted standard for determining current market price is to survey the market area with considerations for quantity and quality for a "going price" of the goods and services in question.In a widely cited case, the FTC went after a Baltimore roofing contractor in the early 1970s successfully alleging the contractor was overcharging consumers to reroof their homes.

In order to rent out a home in the City of Detroit you need a C of A (Certificate of Acceptance) and a C of O (Certificate of Occupancy) therefore you can't collect rent.