You are (mostly) correct. It is pre-symptomatic transmission that has driven most of the spread. By comparison, asymptomatic carriers have been shown in studies to spread the virus much less effectively. People can still get infected after being vaccinated (or having recovered naturally), but they are far more likely to have a truly asymptomatic case and therefore less likely to spread the virus.
That's an interesting distinction I will look into more. Thank you for the reply.
If this is the case, I stand by my questioning of OP's statement: "a vaccinated person, like anyone else, can only transmit the virus if they have a symptomatic breakthrough case."
This one is great because it really brings to light the issue with deciphering the data...
"Since asymptomatic infections represent a large fraction of the infected population, they contribute substantially to community transmission in the aggregate together with presymptomatic cases, even when they individually transmit at a low per capita rate."
