Vaccinated index cases infecting others in the same household are only one scenario, and in that particular scenario, the study found no impact on spread. The study did find that vaccinated household members were less likely to be infected (SAR 25% vs. 38%) and that vaccinated cases had a faster rate of viral load decline - both of these findings (especially the first one) also relate to spread.
(It's arguably a bit surprising that the faster rate of viral load decline did not have an impact on the SAR for vaccinated index cases - one could make a (hopefully) reasonable hypothesis that this would matter more outside of household settings and thus still have an overall impact on spread, but that's not backed by any data from this study.)
There's also a world of difference between not "ignor[ing] the vaccinated population as a possible and relevant source of transmission" and saying that it doesn't stop spread to any significant degree. It's not binary.