This last string of spoilers is about the end of the third book and one PoV of the fifth book, if anyone is wondering.
Anyway, it struck me as needlessly contrived when I read that. There must certainly be easier ways to smuggle poison into the wedding banquet, not to mention that having Olenna poison the wine seems terribly risky, when she is in the top three most suspicious people in Cersei's feverish mind. Littlefinger could indeed be lying, he's patologically incapable of telling the truth, and this version of the events puts Sansa in a difficult situation, with LF as the only person she can trust. But then, if what he tells is a lie, what's the point of the hair net?