[xzins]

The scholars have found that in quotes from rabbinic writings around the 5th century A.D., the phrase was longer: "those who swear falsely in my name."

A questionable 5th AD quote would be some 800+ years older than any OT writing, so it's hardly reliable.

[Buggman]

That, or the rabbis intentionally inserted "by My Name" in their quotation because they considered that to be the real meaning of the shorter phrase, possibly by way of cross-referencing with Zec. 5:4. Since there are no quotation marks in Hebrew or Aramaic, it's easy to become confused on that point.

On using the LXX to "fix" the Hebrew text, that'd be like trying to reconstruct the "true" Greek NT by using the KJV as a source--or worse, the NIV, since the LXX often paraphrases and interpolates to better explain the text to its audience.

Shalom