I can't say that I've seen any Pfizer narratives suggesting that the vaccine protects other (unvaccinated) people from catching the virus. Conversely, their reports typically highlight the fact that even people who have had the vaccine can in fact catch the virus again. They can also remain A symptomatic (where they suffer no side effects whatsoever), where the possibility of them passing the virus on the someone else is a real threat.
This is true with all vaccines, and common knowledge among epidemiologists and the pharma industry (and WHO) right now.
I could be wrong, but I think this is why they want everyone to get vaccinated.