It was the information given to people, by the very experts they're taught to look to for truth, to convince them to get the vaccine. It's really more than a promise, in fact -- it's a statement that said "we have studied this, and are convinced that it's 95% effective". Further, the efficacy was not stated as a range, with a lower bound of 50% or less. Rather, we were told _it works_. The CDC director saying last Spring "if you've gotten both doses, you cannot catch Covid, and you cannot spread Covid" was not an intentional lie -- but it was a promise made very clearly, but unfortunately overly optimistic.
