No they might not have lied.
Even after being vaccinated, we can carry the virus and spread it to others - those vaccinated and those not vaccinated. Those fully vaccinated with a breakthrough infection can be either symptomatic or asymptomatic.
Occasionally, people who have been fully vaccinated can also end up in the hospital or even die - not often, presently, but the efficacy of the vaccine(s) against the Delta variety is waning - thus the talk for a booster. Scientist just have to agree on why the vaccine(s) efficacy is waning.
Thus Everybody needs to wear a mask - a KN95 mask, at least, when around others - vaccinated or not - unless you are outside with a lot of social distancing.
It's Always Something . . . . Roseanna Roseannadanna