Here we'll talk about witnesses who know about what happened in a certain case, but the court wouldn't accept testimony from them. How does that play out in terms of Shevuat HaEdut (oath of testimony) and the need to bring the korban (sacrifice) for lying? The Mishnah says, “If somebody said to two people, ‘I am putting a swear on the two of you,’ and he names them so-and-so and so-and-so, ‘if you know testimony that would be helpful to me, come forward and testify for me.’” And they respond to him, “We swear we don't know any testimony. We don't have any information that would be helpful to you.” But in reality, they do know testimony that would be helpful to him, but not as direct witnesses. Rather, they heard it from somebody else who was a witness. So they're second-hand here. They didn't see it directly, but somebody they know did see it directly and passed on that information to them. This type of testimony would not be eligible or accepted in court.
Another case: even if they did see the event in question themselves, one of them wasn't eligible to testify because he was a relative of somebody involved, and a relative can't testify. Or he was a disqualified person whom the Beit Din (court) wouldn't accept his edut (testimony). In these cases, Harei Eilu Peturin: the witnesses would not be obligated to bring a korban for their lie about them not knowing knowledge, because their testimony wouldn't have been accepted in court. If the testimony wouldn't have been accepted in court, either because they didn't see it themselves and weren't eyewitnesses, because they were family members of somebody involved, or because they were generally pasul (disqualified) to give testimony, then the whole idea of them lying over here really becomes irrelevant. We say it's only if they could have given testimony in court and they held it back. In this case, they wouldn't have been able to give testimony in court. So, therefore, their holding it back isn't something that would obligate them to bring a korban.