This is one of the most persistent pieces of misinformation I've seen, especially in the face of clear data.

The reduction in transmission rate for the vaccinated is 89%. Even for someone with a breakthrough infection of the more contagious Delta variant being vaccinated means a 63% reduction.

https://www.newscientist.com/article/2294250-how-much-less-l...

You are correct, it seems, if this trial is done correctly. https://www.medrxiv.org/content/10.1101/2021.10.14.21264959v...

It's become reflexive whenever people claim it stops transmission because all evidence for it is very very recent, while the claim of stopping transmission started to be used with authority as early as Feb 2021 with absolutely no evidence. Not even Pfizer's press release in 2020 tried to claim they even researched it, let alone had a conclusion, despite people nowadays claiming otherwise.