Given they get infected in the first place, right? It is a posterior probability. This is the "Interpretation" paragraph from the linked Lancet paper:
> Vaccination reduces the risk of delta variant infection and accelerates viral clearance. Nonetheless, fully vaccinated individuals with breakthrough infections have peak viral load similar to unvaccinated cases and can efficiently transmit infection in household settings, including to fully vaccinated contacts. Host–virus interactions early in infection may shape the entire viral trajectory.
Also note that the study is about household settings (which are responsible for the majority of transmissions according to the article), where the exposure is prolonged, and the faster decline of the viral load in vaccinated individuals with breakthrough infections cannot make much difference.
“can be” in that sentence just means the range of potential degrees of infectiousness overlap, which is not quite literally semantically null, but close enough as to make no practical difference.
> Vaccination reduces the risk of delta variant infection and accelerates viral clearance. Nonetheless, fully vaccinated individuals with breakthrough infections have peak viral load similar to unvaccinated cases and can efficiently transmit infection in household settings, including to fully vaccinated contacts. Host–virus interactions early in infection may shape the entire viral trajectory.
Also note that the study is about household settings (which are responsible for the majority of transmissions according to the article), where the exposure is prolonged, and the faster decline of the viral load in vaccinated individuals with breakthrough infections cannot make much difference.