What the law really says and how that might change
Any time there is an outbreak of preventable disease in this country we remember that there is no such thing as a perfect vaccine. They can fail, if rarely, and it only takes a moment of exposure to catch an airborne disease from an incautious carrier.
According to the California Department of Public Health (CDPH), at least 17 reported cases of measles in the current outbreak occurred in persons who had been vaccinated for the disease, a tiny number against the vaccinated population, but they had taken steps to avoid the disease and caught it anyway. They are not responsible for their sickness, but does that mean the person who exposed them is?
The answer may be yes, if you can prove they acted carelessly.