“Individuals who have had two vaccine doses can be just as infectious as those who have not been jabbed.”

https://www.bbc.com/news/health-59077036

(Article contains link to the Lancet study)

That happens in breakthrough infections, and the goal of the vaccine is to reduce the number of breakthroughs, which it does successfully.

From the Lancet study linked in the article:

> The SAR in household contacts exposed to the delta variant was 25% (95% CI 18–33) for fully vaccinated individuals compared with 38% (24–53) in unvaccinated individuals.

That's a misleading line, referring to peak viral load. If you read the rest of the article (or probably the study abstract), you will see vaccinated people are infectious for less time.

It’s less, but you have to factor the ^(n) interactions over years.

Vaccinated people will spread without even knowing, this is already the main way of spread in many areas with very high vaccination rates.

This is exactly right and is maybe the primary factor in why infection rates sky rocketed (year over year) in places that had high vaccination rates.