That might very well be true and as a vaccinated person myself I hope it is true.

But how does that affect my conclusion that the vaccinated still have to be careful and herd immunity is unlikely to be a thing? A false sense of security is a problem in itself.

You seem to be making a few assumptions. The other half of the story could easily be that vaccinated individuals are equally likely to harbor detectable virus, I'm just pointing out that there is a big other factor to consider before we know how important vaccination is with regards to herd immunity and benefit (or risk) to one's community.