Ms O'Leary said she was entitled to voice her political opinions.
"Social media has enabled all sorts of people to share different views and more importantly has opened up council to a new group of people.
"Social media by its very existence invites comment."
She pointed out that Hamilton Mayor Julie Hardaker put her own views in her opinion piece in the council's ratepayer-funded newsletter City News which was much more "serious" than commenting on social networking sites.
Followers on her Facebook page had also supported her rights to speak out.
But Hamilton City Council customer relationships general manager Jason Dawson said he had only "flagged" the issue with councillors yesterday as something they might want to discuss in the future.
In the meantime elected members would be treated "as normal citizens".
The public is free to comment on the council's Facebook page and the council removes only posts deemed to be defamatory, racist, sexist or offensive.
"What I said was 'an example would be if she did say something against a decision or a resolution, is she's entitled to have her view but not on the Hamilton City Council Facebook page. She's got her own channel'."
Mr Dawson also planned to investigate if and when Ms O'Leary's post had been removed previously.
The council had asked for social media training, and as part of this would discuss whether a social media policy for elected members was required.
BANNED
Comments banned from Hamilton City Council's Facebook page:
* Defamatory
* Racist
* Sexist
* Offensive language
* Religious views
Staff rules:
* No comments speaking against council decisions.