You are likely blending PMLs with HMLs here, most PMLs lend on a relationship basis and most HMLs underwrite the credit profile and risk of a deal. 

Obviously if the value is low that's one thing, but what if I pay and they deny me for some other reason?

But in the end we bought a big townhouse with low HOA dues for ~$50k under market value.

Learn by doing, not by paying.You can do all the right things after spending $40,000 on mentoring and not end up with any real estate.If you invest in a project.....very low chances you end up with nothing.   

Now, one month later, I’m called to face this situation.My energy level was low.

If the rate is low you'd be much better off finding solutions other than refi (pulling personal loans, second positionAlso, what's your credit looking like?

Great Buy and low interest rate. 3.5% How did you find this deal and how did you negotiate it?

What are some decent areas with low property tax and high occupancy rate?

As we first hand see the demand for student housing with a low supply of affordable options in the area.

I suspected fraud as the property was too nice and the rent was too low.