The article/video was designed to explore that very question. And if you go back and read the first post, you'll see that it was indeed the premise:
Hello? Are you reading the same post I am?
How do you spread a disease? How about this: Inject a few million people with the virus and release them into the population. It's vaccinated people who now carry and spread sickness. Not those who are uninfected. Don't like the sound of that? Sorry. The science holds on this one.
The video also is not about secondary infections and is clearly designed to spread FUD about vaccines. It distorts the words of Anne Schuchat by only showing the parts of the statement and what she was addressing. In fact the end of video it advocates for the rights of parents not to vaccinate.
It seems you're letting ego obscure the matter, because it's a valid question and the observations collected from studies which may not have been designed to directly examine the issue, nonetheless still provide useful information toward clarifying our understanding of that point.
Please. The whole statement is tinfoil hat thinking as if there was a grand conspiracy to spread a disease by vaccinating against it. The question that was stated didn't have anything to do about secondary infections. It wasn't stated whether immunities last as long as once believed. Also one aspect ignored by the anti-vaccine crowd is even if immunities do not last as long, that doesn't negate the fact that the person had immunity and there are much less likely to be infected with a vaccine than without.
A study trying to determine the rate of disease in cats, by default suggests that cats really do exist despite that not being its primary critical goal. Lateral thinking.
Unless that is the entire goal of the study. Extrapolation is a tricky thing in science. The goal of the HIV study was to study how HIV affected particular vaccine by the manufacturer. Trying to extrapolate to what it means for the general population when decades of other research has already answered the same question is bad science.