describe why silver cookware tarnishes, especially in the present of sulfer-containing food such as eggs

You would be correct, boiling water does disinfect contamination.    the property of disinfecting means to kill  germs, bacteria and other pathogens or contamination  that might cause an infection or cause a person to become sickly. a couple methods of disinfecting are using soap, other cleaning supplies or by simply "boiling" the contaminate.  the reason why boiling water disinfects certain attributes is because some cells cannot survive the heat and pressure.