They didn't modify anything. Look at the table. No matter what the results of the experiment they would have come up with the same tree. In actuality the universe of possibilities for this test(3 classes sharing something) is exactly two. All the same or odd man out. All the same results in the preconceived tree and the odd man out is easily handled to give the same tree. That I call Darwininan logic.
If we just had this one piece of data to deal with, then it would make the most sense to say that the great apes are closely related and that humans diverged at some point before the viral insert appearing in the apes. However, the conclusion reached needs to supported by all of the data. The solution these authors propose succeeds in explaining all of the genetic data available.