Some people have asked: how can the singleton return a null pointer?
I'm answering that question. (I cannot answer in a comment because I need to post code.)
It may return null in between two events: (1) the class is loaded, and (2) the object of this class is created. Here's an example:
class X {
    static X xinstance;
    static Y yinstance = Y.yinstance;
    X() {xinstance=this;}
}
class Y {
    static X xinstance = X.xinstance;
    static Y yinstance;
    Y() {yinstance=this;}
}
public class A {
    public static void main(String[] p) {
    X x = new X();
    Y y = new Y();
    System.out.println("x:"+X.xinstance+" y:"+Y.yinstance);
    System.out.println("x:"+Y.xinstance+" y:"+X.yinstance);
    }
}
Let's run the code:
$ javac A.java 
$ java A
x:X@a63599 y:Y@9036e
x:null y:null
The second line shows that Y.xinstance and X.yinstance are null; they are null because the variables X.xinstance ans Y.yinstance were read when they were null.
Can this be fixed? Yes,
class X {
    static Y y = Y.getInstance();
    static X theinstance;
    static X getInstance() {if(theinstance==null) {theinstance = new X();} return theinstance;}
}
class Y {
    static X x = X.getInstance();
    static Y theinstance;
    static Y getInstance() {if(theinstance==null) {theinstance = new Y();} return theinstance;}
}
public class A {
    public static void main(String[] p) {
    System.out.println("x:"+X.getInstance()+" y:"+Y.getInstance());
    System.out.println("x:"+Y.x+" y:"+X.y);
    }
}
and this code shows no anomaly:
$ javac A.java 
$ java A
x:X@1c059f6 y:Y@152506e
x:X@1c059f6 y:Y@152506e
BUT this is not an option for the Android Application object: the programmer does not control the time when it is created.
Once again: the difference between the first example and the second one is that the second example creates an instance if the static pointer is null. But a programmer cannot create the Android application object before the system decides to do it.
UPDATE
One more puzzling example where initialized static fields happen to be null.
Main.java:
enum MyEnum {
    FIRST,SECOND;
    private static String prefix="<", suffix=">";
    String myName;
    MyEnum() {
        myName = makeMyName();
    }
    String makeMyName() {
        return prefix + name() + suffix;
    }
    String getMyName() {
        return myName;
    }
}
public class Main {
    public static void main(String args[]) {
        System.out.println("first: "+MyEnum.FIRST+" second: "+MyEnum.SECOND);
        System.out.println("first: "+MyEnum.FIRST.makeMyName()+" second: "+MyEnum.SECOND.makeMyName());
        System.out.println("first: "+MyEnum.FIRST.getMyName()+" second: "+MyEnum.SECOND.getMyName());
    }
}
And you get:
$ javac Main.java
$ java Main
first: FIRST second: SECOND
first: <FIRST> second: <SECOND>
first: nullFIRSTnull second: nullSECONDnull
Note that you cannot move the static variable declaration one line upper, the code will not compile.