Many of the 2-state machines tend to oscillate between defection and cooperation (for various inputs, including oscillating or static). Tit-for-tat can get locked into a "I defect one round, you defect the other" loop which is less payoff worthy than mutual cooperation.
The presence of many irrational oscillators (that aren't really 'trying' to win the game) in response to fixed inputs I think skews the possibilities; if there are many oscillators, regardless of your inputs, defecting each round gets you (0, -2) vs. mutual oscillations (0, -3). So chasing an oscillator is a bad idea, but a two-state machine isn't able to see past this, I think.