To be fair Liddell never said that. His direct quote when asked about him vs Tyson in their primes is "Boxing, I don't want to mess with the man. MMA, I got no problem. We do a street fight I'm Okay. Boxing I ain't messing with the man".
Liddell was giving a reasonable response of what many fighters would say. It is hard to fault him for that. He is a fighter and was a champion in the UFC so he is going to be fairly confident in his abilities and think he can compete with anybody whether that is the case or isn't. He also is giving a fairly reasonable response. He doesn't have the skill or ability to compete with prime Mike Tyson in boxing. In MMA he has a diverse array of skills and a lot of experience so he at least has ways he can win the fight. Similarly with a street fight he can use more of his tools so he has a chance and he has enough power to put anyone away if he leans cleanly.
As for a hypothetical Mike Tyson vs Chuck Liddell match up. Mike Tyson has a really good chance of stopping Liddell in boxing, mma or a street fight. Liddell isn't very fast and he leaves himself wide open defensively. Mike Tyson was a freak athlete and his speed and power was something else. There would be a good chance that Tyson lands multiple solid shots before Liddell landed anything.