A person approaches two witnesses and says, “I’m putting an oath on you if you don’t come and testify on my behalf.” What was the case? So-and-so told me he was going to give me 200 zuz (a unit of currency), but he hasn’t given it to me yet. So here we have to take note: there’s no promise from that person to hand over 200 zuz. He says he would give it to me, but he’s not obligated to give it to me.
In this case, the people falsely denied knowledge of this testimony. These two witnesses are still not obligated to bring a korban (offering), because witnesses would only be obligated to bring a korban for swearing falsely about a claim on which the defendant they would testify about would be forced to pay if they testified, like a pikadon, like a case of a deposit mentioned in the pasuk (verse).
In our case, though, the person they would testify about—we’ll call him the defendant—even if they gave their testimony, would not be forced to pay. They’re not testifying about an obligation. They’re testifying that the man said he would give it, but there was no obligation on that man’s part. So the fact that they held back their testimony doesn’t really change anything legally. What we say is that they’re patur, they’re exempt from bringing a korban. Their testimony wouldn’t have had an effect anyway, so they would not have to bring this korban.