The vaccine won't stop people from carrying the virus on the persons, like cloths hands things the vaccine won't control. People might not be breathing it but they can still be a carrier
AstraZeneca says theirs stops people from being infectious. It's not just stopping people from being "sick" - it's stopping the virus from multiplying and thus transmitting.
Touching something that someone infectious touched, and then touching someone else, has not been a significant transmission factor. Breathing in aerosol that someone infectious expelled, is the biggie.