Vaccine: you'll get COVID but no symptoms?

They don’t know yet. This guy is just saying they haven’t proved vaccinated people aren’t infectious.

Making you be asymptomatic or very mild symptoms is used as the mark of a successful vaccine because that’s a more readily thing to test. How infectious people are is something that akes more time and effort to figure. Generally though, a vaccine that helps well with symptoms is probably good for lowering infectiousness.