Rashi DH R' Akiva writes that the witnesses do not become Zomemim unless all of them are Moozam. So it is not the case that the 3rd witness is only punished by asociation, since the 3rd was also found to be a liar and thereby also an EZ. Rather, the chidush is that even though the 3rd witness is not necessary; since the victim could have been condemmed on the basis of the testimony of the first 2 witnesses alone; nevertheless the 3rd witness is also punished. In summary, the 3rd witness is a liar, but his testimony is unecessary. Even so he is punished because he is part of the malicious team.

If the 3rd was not proved to be a liar nobody would be punished.

Dovid Bloom