No, getting vaccinated is not stops anyone from transmitting disease, it is obvious. Virus gets to breathing system of vaccinated people same as for unvaccinated, and replicates there for 4-6 days. Then they either have a vaccine breakthrough, or vaccine-boosted immune system kicks in and defeats the virus in next 2-3 days. All this time the vaccinated host is as dangerous for others as unvaccinated.
I hope you didn't know it or didn't think it through, otherwise mention of Fox News seems to me a blatant hypocrisy. Either way it was an unnecessary ad hominem attack.