I am considering purchasing 2 duplexes (4 units) owned by the same person. 

You're not also flipping the property, so the cost of money isn't really your personal issue.

It rents for $900 per month and provides us a 25.63% Cash on Cash Return or 11.16% Cap Rate (usually only used in commercial realm, but we do commercial loans on packages of homes to avoid using our personal credit).

Look into "wholesale" strategies...I don't personally know anything about that though hahahaha.

I called my personal real estate agent and they are unlikely going to be able to underwrite the house as its current condition is "below average."

Write it up as a personal letter.When you do all that, then contact a local RE Agent to give you a list of all the houses in that neighborhood that have sold in the last 5 years with all cash.

I managed to get 2 cash buyers from personal relationships.

I searched through Facebook profiles to see if I could find a picture of the house, or anything that eluded to that person being the correct owner.

This is only my personal experience so don't let me stop anyone from doing what you guys and gals want to do.With respect to J Martin's guest who were loud which caused us to lose one of our tenants.

To be sure, there seems to be a danger of being the last person holding the bag.