Strange C++ boolean casting behaviour (true!=true)

Just read on an internal university thread:

#include <iostream>
using namespace std;

union zt
{
 bool b;
 int i;
};

int main()
{
 zt w;
 bool a,b;
 a=1;
 b=2;
 cerr<<(bool)2<<static_cast<bool>(2)<<endl;                      //11
  cerr<<a<<b<<(a==b)<<endl;                                      //111
 w.i=2;
 int q=w.b;
 cerr<<(bool)q<<q<<w.b<<((bool)((int)w.b))<<w.i<<(w.b==a)<<endl; //122220
 cerr<<((w.b==a)?'T':'F')<<endl;                                 //F
}

So a,b and w.b are all declared as bool. a is assigned 1, b is assigned 2, and the internal representation of w.b is changed to 2 (using a union).

This way all of a,b and w.b will be true, but a and w.b won't be equal, so this might mean that the universe is broken (true!=true)

I know this problem is more theoretical than practical (a sake programmer doesn't want to change the internal representation of a bool), but here are the questions:

1. Is this okay? (this was tested with g++ 4.3.3) I mean, should the compiler be aware that during boolean comparison any non-zero value might mean true?
2. Do you know any case where this corner case might become a real issue? (For example while loading binary data from a stream)

EDIT:

Three things:

1. bool and int have different sizes, that's okay. But what if I use char instead of int. Or when sizeof(bool)==sizeof(int)?

2. Please give answer to the two questions I asked if possible. I'm actually interested in answers to the second