The difference between casual human conversation on a late night panel show and the strict precise statements in actual papers.
The educated with real world exposure to weed eradication, stock control,. past use of vaccines, etc didn't take the "do not carry the virus, don't get sick,..." absolutely literally as if it was deified bible quote either.
They heard that as saying given the data to hand right now (context) that data suggests (qualifier) that the vaccinated aren't carrying the virus nor getting sick (in contrast to those unvaccinated .. as in there is a visible stark difference).
A chat on a late panel show IS NOT "the science" and a paper on the stats coming back from trials would use actual percents, p-values, etc and make it clear.