I think you will find that the Fair Work Act's Freedom of Association provisions explicitly override anything contained in an industrial agreement such as an EBA or an ancillary document such as an employee "code of conduct" booklet.
If what he had to say was factual you may have a point - so it's a pity that he published misinformation designed to incite support of an opinion. That others have the same opinion does not make it fact. So, not really a leg to stand on is there...