Hmmm. But with Mr. Kaplans history with liz and when she discusses it it would seem that she knew Red and Katarina from years before. Or maybe she knew this secret
Another point is that DNA was negative.
This was my theory for close to a year already, (FYI it explains Reds feminine personality perfectly, lol) if you have a look at the cryptic episode Cape Cod you can understand it perfectly based on this theory, it is basically Red saying goodbye to his old self (aka katerina) and becoming his new persona as Red.
In regards to the DNA, keep in mind the DNA test on him being Liz`s father WAS a match but the DNA of him being the real reddington was NOT, which is perfectly in sync since they were testing for family DNA so it showed a close enough relationship and hence they assumed its her father which would be in line with this theory since her mothers DNA would show this they were just not thinking of terms of maybe this is her mother, and why it was not a match with the real Red is simple because he isnt he is the Fake Red previously known as Katarina...this is what he whispered to Kurk (katarinas Ex husband) when he wanted to kill him since he believed it was the real Red who cheated with Katarina on him, successfully changing his mind and allowing his life to be spared since he would not want to harm katarina...
Anyone that has any questions or points as to why they believe that this theory is not in line with previous facts or details please share as im pretty confident this is the answer to the puzzle, and I believe just about everything can be reconciled using this theory.