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”.

> 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