Blackmail?

At first I felt the same way. The husband's phone conversation with the building manager and the flashback of Yoon instead of her friend on the balcony would suggest this. However, one of the main issues with Yoon is that no one believes her about her visions, especially her husband. My speculation is that the flashback is her husbands thoughts, thinking Yoon was actually behind the murders. Furthermore, the flashback of Yoon's friend being afraid of the babies would imply she's more capable of killing the babies.

Yun's husband does not believe her, a point made throughout the film, therefore he feels the need to "payoff" someone to "lie" on the witness stand. Yun didn't kill the kids, but her ability to reveal peoples dark secrets drove the friend mad.

As far as I saw it the 'blackmail guy' was willing to NOT say that he thought the woman who killed the babies was mentally disturbed at the time (thus risking the 'innocent due to insanity' verdict) if he got something from the husband. As he did not get anything, he stated he thought the woman looked deranged and out of it.