I think from the individuals which were recorded as you said, very few nestlings had deformities with there beak, but however it was found that there was slight problems in a tiny percentage of individuals.
Also the pairs which did breed with such deformities showed very odd behaviour in the nest such as 'with eggs strewn erratically across the nest' this would in turn affect the breeding sucess.
Selenium, polychlorinated biphenyls (PCBs), polychlorinated dibenzo-p-dioxins (PCDDs), and polychlorinated dibenzofurans (PCDFs) were all found in the birds with deformed beaks, however, as i read it as from the samples which they did on the sunflower seeds non of these showed any detectable concentrations of these compounds. 'Chickadees may be ingesting HCB and lead from sunflower seeds but are more likely accumulating PCBs from other sources'.
They did however find PCBs were ubiquitous in chickadee egg. Therefore, as you said, the diets of the birds during the winter could cause and increase in PCB's in the egg which in turn remained in the invididual causing bill deformities. As they didnt however state this was the case, the source of the PCB's could have come from anywhere, therfore possibly genetic or from another contaminated point source.