Is there anyone still alive on the show that knows of Baelish's role in Ned's failed coup and would be willing to divulge that information? I'm wondering how Sansa would come by such sensitive intelligence, especially now that she is back in the North with no ties to King's Landing. Counting off people who knew of Baelish's involvement, we have:

Janos Slynt - beheaded by Jon Snow for something completely unrelated (Jon unwittingly exacts revenge for Slynt's betrayal of Ned)

Petyr Baelish - very alive, not stupid (also unlikely to divulge given he is the perpetrator)

Cersei Lannister - alive, positively unhinged, semi-frequent Baelish patron (if they have her specifically mention the betrayal in a ravenscroll and Sansa intercepts/finds it when Baelish isn't looking, that would be lame)

Varys - alive, constantly plotting to advance the Targaryen Restoration (could use the information as leverage to gain Sansa's support and implicitly the support of the North -- though he is very cautious of Baelish, in the past he seemed reluctant to outright kill him...doing this would be dooming him to certain death)

Also, possibly Tyrion - when he is spreading misinformation among his confidantes (Baelish, Varys, and Pycelle) in S2 he mentions Baelish's help "in the matter of the succession"