The scenario may be possible, there is a thing called an Asymptomatic Carrier, the most famous being Typhoid Mary, these people have a disease that doesn't effect them but they can still pass it on to others. As I understand it any disease, whether viral or bacterial, can have asymptomatic carriers, I know people can be asymptomatic carriers of the mumps virus as well as typhus bacteria.
Quarantine measures in these cases are tricky, no-one, even the carrier knows that they're sick until after the people around them start dropping, and it can be very hard to tie the disease to a specific source, delaying quarantine implementation further. In the case of Typhoid Mary they eventually had to jail her because they couldn't convince her that she was making people she cooked for ill. Depending on the latency period, how long it takes between host infection and the first symptoms of the disease, virulence, the speed and efficiency with which the disease spreads and it's lethality by the time they know that they need a quarantine they could all be dying.