Why to synchronize on SynchronizedMap or SynchronizedCollections?

I am referring to question asked here and using authors code example, now my question is

1. Why does author uses synchronized(synchronizedMap), is it really necessary because synchronizedMap will always make sure that there are no two threads trying to do read/put operation on Map so why do we need to synchronize on that map itself?

Would really appreciate an explanation.

  public class MyClass {
  private static Map<String, List<String>> synchronizedMap =
      Collections.synchronizedMap(new HashMap<String, List<String>>());

  public void doWork(String key) {
    List<String> values = null;
    while ((values = synchronizedMap.remove(key)) != null) {
      //do something with values
    }
  }

  public static void addToMap(String key, String value) {
    synchronized (synchronizedMap) {
      if (synchronizedMap.containsKey(key)) {
        synchronizedMap.get(key).add(value);
      }
      else {
        List<String> valuesList = new ArrayList<String>();
        valuesList.add(value);
        synchronizedMap.put(key, valuesList);
      }
    }
  }
}