She actually complained in one sentence about the water damaged walls and her son's asthma.

People are ADD and sometimes don't read sentences, they can look at pictures/charts.     

His very last sentence was something to the effect of "there are tons of buyers and not very many sellers, so by purchasing houses straight from sellers we will bring value to the market."

I think you just answered your own original question with that last sentence of your why. 

Being stuck in the terminal at JFK during an 8 hour weather delay is normally a prison sentence.

The seller has provided me with a 2013 appraisal that is quite thorough and has many comps and valuation approaches, but obviously is 5 years old.He also told me that they have a recent appraisal that was done and when I asked to see it, all I received was a couple of sentences that used the income valuation approach to come to the same price he originally offered.My main question is what value does the income valuation approach have to a property that could potentially be vacant in 3 years?

This last sentence tells you everything you need to know.

She finally typed up a single sentence addendum that says, "Owner and seller agree that renter will move out before closing," , and continues to insist that her broker says, "all of our bases are covered."

I'm not an attorney, so the next couple sentences are just a layman's interpretation.

What that means is that she is likely about to spend some time in jail, pre-trial (does not sound like she can afford bail,) and perhaps be sentenced to a term.