That is not true. Her response was:
"Well, first of all there’s a difference between an executive role and a legislative role. Council serves as a legislative body, not an executive body. While I have not personally written any on the State level, mayor, I have worked side-by-side with Mayor Teresi and you to try to do what’s best in the legislation presented to us to protect the residents and the community of the city. So, me personally writing legislation? No. Mayor, I don’t feel that’s my role as a council member, but to help sponsor those legislations, that we worked on a unified body or with the administration through the years. Absolutely glad to be a partner in."
She clearly took "legislation" to mean State legislation, which is where that term is commonly used, rather than to mean ordinances, resolution, budgets, etc. that are passed by the city council. She didn't say anything about writing laws being the job of the executive.