Do you understand that "reduce" is not synonymous with "eliminate"?

Because an acknowledgement that fully vaccinated people can spread Delta is not a refutation to the claim that it reduces the spread.

Even the paragraph you quoted says "However, like prior variants, the amount of viral genetic material may go down faster in fully vaccinated people when compared to unvaccinated people. This means fully vaccinated people will likely spread the virus for less time than unvaccinated people."

> Fully vaccinated people with Delta variant breakthrough infections can spread the virus to others. However, vaccinated people appear to spread the virus for a shorter time

That does bot support your claim that “It is a proven fact now that vaccinated folks spread just as much as non-vaccinated.”

It says:

* Vaccinated people are leas likely to get COVID, even with the Delta variant.

* Vaccinated people who do get breakthrough infections remain infectious for a shorter time than unvaccinated, even with Delta

It does note that vaccinated people with breakthrough infections can spread Delta, but that is not the same as “just as much as the unvaccinated”.