Say you have:
class a { void f() }
and
class b extends a { private int x }

In normal static references there is no way for method f() to reference x in
class b. However, with the reflect methods f() could be looking at x if f()
was called on an object of type b. Shouldn't access to this private variable
be allowed in this case??

Here is some code which demonstrates this:
import java.lang.reflect.*;
 
public class test
{
  public static void main(String argv[])
  {
    test2 t2 = new test2("hello", "goodbye");
    t2.seeFields();
  }
 
  public void seeFields()
  {
    Object obj;
    Field[] fields = getClass().getDeclaredFields();
    for (int i=0; i < fields.length; i++)
    {
        String field = fields[i].getName();
        System.out.println("getting " + field);
        try
        {
            obj = fields[i].get(this);
        }
        catch (Exception ex)
        {
            ex.printStackTrace();
            continue;
        }
        System.out.println(field + ": " + obj.toString());
    }
  }
 
}
 
class test2 extends test
{
    protected String prot;
    private String priv;
 
    public test2(String x, String y) { prot = x; priv = y; }
}

The output here is:
getting prot
prot: hello
getting priv
java.lang.IllegalAccessException: test2
        at test.seeFields(test.java:22)
        at test.main(test.java:9)