Why do I need a memory barrier?

C# 4 in a Nutshell (highly recommended btw) uses the following code to demonstrate the concept of MemoryBarrier (assuming A and B were run on different threads):

class Foo{
  int _answer;
  bool complete;
  void A(){
    _answer = 123;
    Thread.MemoryBarrier(); // Barrier 1
    _complete = true;
    Thread.MemoryBarrier(); // Barrier 2
  }
  void B(){
    Thread.MemoryBarrier(); // Barrier 3;
    if(_complete){
      Thread.MemoryBarrier(); // Barrier 4;
      Console.WriteLine(_answer);
    }
  }
}

they mention that Barriers 1 & 4 prevent this example from writing 0 and Barriers 2 & 3 provide a freshness guarantee: they ensure that if B ran after A, reading _complete would evaluate to true.

I'm not really getting it. I think I understand why Barriers 1 & 4 are necessary: we don't want the write to _answer to be optimized and placed after the write to _complete (Barrier 1) and we need to make sure that _answer is not cached (Barrier 4). I also think I understand why Barrier 3 is necessary: if A ran until just after writing _complete = true, B would still need to refresh _complete to read the right value.

I don't understand though why we need Barrier 2! Part of me says that it's because perhaps Thread 2 (running B) already ran until (but not including) if(_complete) and so we need to insure that _complete is refreshed.

However, I don't see how this helps. Isn't it still possible that _complete will be set to true in A but yet the B method will see a cached (false) version of _complete? Ie, if Thread 2 ran method B until after the first MemoryBarrier and then Thread 1 ran method A until _complete = true but no further, and then Thread 1 resumed and tested if(_complete) -- could that if not result in false?