Principals have adopted the one-hour weekly sessions - which cost parents about a couple of hundred dollars per term - without being shown the course content. Fairfax Media has been told Ms Slattery refuses to show the principals the content, claiming this would breach her intellectual property.
Ms Slattery, who sent her statement to Fairfax Media via text because she deemed a phone conversation longer than six minutes unsafe, confirmed that her views on vaccinations were not in the curriculum.
She claimed she almost died and her husband "probably died" from "radiation poisoning", while other gifted people have become ill due to "neurological connections vibrating at alien frequency". She claims she is still alive because she moved into a caravan with no power and takes anti-radiation herbs.
"None of this is in curriculum. It was there to support parent choice as court cases have proved link of vaccines to autism and [a] low immune system," she said.
Ms Slattery also links leukemia and brain tumours to radiation from Wi-Fi and microwaves and has written to Education Minister James Merlino about the need to remove microwave radiation from schools.
"If you have a very clever child beware-thinner skulls and more moisture for the microwaving," she said on her website.
Education Minister James Merlino said Ms Slattery's claims were "absolutely ridiculous".
"We don't teach this sort of rubbish in Victorian schools ... it is my expectation that such nonsense is not and never will be reflected in resources distributed to Victorian schools."
Health Minister Jill Henessy said evidence that vaccinations save lives is "crystal clear".
"The best thing a parent can do to keep their child well and healthy is to immunise them against preventable diseases," she said.
"People pedalling anti-vaccination myths have no place in our health system or our education system."
The original suggestion that the MMR vaccine might be linked to autism was made in 1998 report which was shown to be fraudulent, and was retracted by the medical journal The Lancet.
The finding has been repeatedly debunked in other academic papers, including a 2014 paper by the Sydney University which was endorsed by the Australian Medical Association.
Simon Chapman, an emeritus professor in public health at the University of Sydney, said Ms Slattery's ideas about the danger of Wi-Fi were "total quackery".
Professor Chapman, who has just released research analysing every brain cancer diagnosis in Australia, finds that a spike in diagnoses in the older age group predates mobile phones, and was likely a result of improved diagnostic procedures.
"There is no evidence of any rise in brain cancer in any of the under-age groups, let alone children."
Anny Lawrence, the principal of Brighton Primary School, which offered the program after-hours three times a week, said she was not aware of Ms Slattery's controversial views.
"My nurse would go crackers," she said.
Ms Lawrence said when she started at the school in 2009, the program was being offered during school hours, but she moved it after school so that students who could not afford to attend would not be excluded. The program ended at the school in 2014 due to low enrolments.
Linda McIver, who is a parent of gifted student Jenna at Brandon Park Primary, alerted the school to the post about vaccinations after the school announced that it would use Wise Ones. The school axed the program instantly.
"I was horrified, I'm desperate to find an extended activities [program] for my girls but there are so few out there. Schools aren't resourced to provide much for really gifted kids ... but if you tell people vaccinations are dangerous, that costs people's lives. That is non-negotiable," Ms McIver said.
A Victorian Education Department spokesman said: "Schools are responsible for choosing curriculum resources and programs that best meet the needs of their communities and help students reach their full potential".
"WiseOnes is used by a small number of schools as a resource to help gifted students succeed and does not contain any reference to either vaccinations or Wi-Fi.
"The Department's Suitable Teaching and Learning Resources guidelines help schools determine whether individual programs are right for their classrooms."