Why does a sudden scare sometimes cure hiccups? 

Hiccups are spasms of the muscles in the diaphragm controlled by the vagus nerves. The spasms occur when the nerves are irritated, such as with a full stomach, carbonated water, etc.  It is sometimes possible to stop the spasms by giving the vagus nerves other tasks to perform. Since a sudden scare sends a host of signals down the vagus nerves to slow the heartbeat and decrease blood pressure, this distraction often causes the nerves to forget about the spasms and the hiccups to stop.