Ryan8bit, while Tyreese will not forget, he was part of the decision to kill Lizzie, so he should not "keep one eye open" (so to speak), or be suspicious around Carol, since he now knows what it means to take action that will save lives. The problem with a man like Rick is that he's still thinking like all laws from the pre-ZA still apply...at least where others are concerned.
Remember, he was willing to hand Michonne over to the Governor, knowing that was a death sentence, only to protect his own interests. At least Carol was dealing with a genuine threat to the entire prison community (if allowed to turn / get loose), as opposed to Rick, who tried to place a non-threat's head on the chopping block.
He seems to be a "do as I say, not as I do" man, which is why Carol has the moral high ground between the two. Even in the Lizzie case, Carol was protecting humanity...not just her own interests from a local psycho in Rick's case (whether that was Shane or the Governor). She was/is seeing the bigger picture, and protecting as many lives as possible. If she reunites with Rick, and he still takes a stand against her, then he's totally divorced from rationality.