That is not the case.
https://www.nature.com/articles/d41586-021-02187-1
"“The bottom line is, this can happen — it can be true that vaccinated people can spread the virus. But we do not yet know what their relative role in overall community spread is,” says co-author Thomas Friedrich, a virologist at the University of Wisconsin–Madison."
Vaccinations may (or may not) reduce the propensity of vaccinated people to spread Delta but it's very clear at this point vaccinated people can spread Delta to some degree.
