the parallel wiring meant the pickup is wired in parallel to another set of pickup, its not one humbucker itself in parallel.
Similary, when anynoe mentioned out of phase wiring, it meant one pickup is wired out of phase with another pickup. By itself, just one pickup cant be parallel or out of phase by itself, it will be the combination of 2 pickups with variation in the wiring that determined each the function
humbucker rid of the hum coz of the way 2 single coil are put together in one package(as a double coil pickup), "reverse wound, reverse polarity", RWRP in short. It doesnt matter whether is it in serious or parallel to another set of pickup. By itself, the RWRP arrangement of the "2 single coil" in one package already is hum cancelling
Theres an entry on wikipedia for humbucker stuff and why the cancellation of hum thats worth reading if anyone interested.