Mr. Polk is indeed getting into semantics over what an "oath" is. He's using the "kitchen sink" approach to trying to block this ballot initiative.
But,
IIRC, when you sign a ballot petition, you are affirming or attesting to the fact that you are a qualified voter, or will be a qualified voter, in the election district (the City of Lakewood in this instance) on the date of the election the ballot issue would be voted on.
A good petition circulator will remind you to read all of the fine print. Not just what the proposed ballot language is.