"I recently saw a show that said genetic differences were a probable cause of why some survived the bubonic plague and others didn't." I don't know about this but, I don't doubt it either. There were many, many plagues and some would have had immunity.
delta 32
http://www.pbs.org/wnet/secrets/case_plague/ Local Eyam lore tells befuddling stories of plague survivors who had close contact with the bacterium but never caught the disease. Elizabeth Hancock buried six children and her husband in a week, but never became ill. The village gravedigger handled hundreds of plague-ravaged corpses, but survived as well. Could these people have somehow been immune to the Black Death?
Dr. Stephen O'Brien of the National Institutes of Health in Washington D.C. suggests they were. His work with HIV and the mutated form of the gene CCR5, called "delta 32," led him to Eyam. In 1996, research showed that delta 32 prevents HIV from entering human cells and infecting the body. O'Brien thought this principle could be applied to the plague bacteria, which affects the body in a similar manner. To determine whether the Eyam plague survivors may have carried delta 32, O'Brien tested the DNA of their modern-day descendents. What he found out was startling ...