interpretation if it were not for Jane Fairfax's confession to Emma in Chapter 52.She knows that her resever and coldness were a breach of the code of civility. She knew she had acted without regard to the small courtesies that civility required.And she was aware that Emma knew she had been deficient.

May I refer you to this from Chapter 52:

"You are very kind, but I know what my manners were to you. So cold and artificial! I had always a part to act. It was a life of deceit! I know that I must have disgusted you."

Prior to this ,in the same Chapter ,when they meet in Miss Bates apartment this descrption is given:

"...a moment afterwards she[Emma-JW] was met on the stairs by Jane herself, coming eagerly forward, as if no other reception of her were felt sufficient. Emma had never seen her look so well, so lovely, so engaging. There was consciousness, animation, and warmth; there was every thing which her countenance or manner could ever have wanted....

Jane Austen placed a lot of emphasis on courtesy,and IHMO, abhorred coldness and artificial manners.Jane Fairfax was guilty of this towards Emma, and,even though she had a dangerous hidden agenda, Emma rightly considers her coldness and refusal to join in the courtesies of a conversation( it is, after all, a two way thing)as evidence of her reluctance to be civil.