Not only would I have switched lines when I heard the beep but I wouldn't have even been on the phone with anyone with the possibility of a kidnapper calling about my missing child.
Then how would you know if someone was calling you about the child? Many people might react by GETTING ON the phone to call friends, relatives and others to let them know what was happening or to enlist support. People have to call employers if they work to report off work. They may need to call doctors for medications or to collect medical records for the missing child. Other family members may need to cancel obligations. Some people might reach out for comfort or just to feel normal. You are right about what YOU would do, but that doesn't serve to predict what others would do--or why they would do it.
When a family is in crisis, it doesn't mean that all life stops; it means that a horrific new stress is added to the already stressful life--jobs, raising children bills and debt, marital trouble, illness, problems at work, aging parents, etc. Do you think most people with missing children can stop working at their jobs, shopping for food, bathing the other kids, paying their bills?
For what it's worth, most people don't think well under stress. When my mother was hospitalized over Thanksgiving, I parked my car in the visitor's lot. Seven hours later, I looked for my keys as I was exiting the hospital, but I couldn't find them. I backtracked all through the hospital looking for them. Then it occurred to me that I might have left them on the seat of the car. Nope. I left them in the ignition. And the car was still running. With the door unlocked.
Did I leave my car unlocked, running with the keys in the ignition because I wanted someone to steal my car? No--because I was under enormous stress. Not to put too fine a point on it, but I'm not stupid. I handle complex situations and solve problems every day. But put my mother in the hospital and I was toast. No one at work had any idea that I was as bad off as I was, because I am one of those who are good at "looking OK." That's how we keep from flying off the earth in bad times. It doesn't mean that we are indifferent, just that we are DIFFERENT from people who cease to function in any other areas when crisis hits. Neither response to crisis says a thing about how much the missing or the ill or the dead are or were loved.