How did Bud White survive a shot in the chest in L.A. Confidential?

In L.A. Confidential, an unsuspecting Bud White, while trying to aid Ed Exley, gets shot thrice by Dudley at the Victory Motel shootout.

The Three Shots:

• Bud pushes Ed out of the way. Gets shot, presumably in the left arm, as we later see his left arm is in a sling.
• As he rushes towards Dudley, he is shot again, in the chest (this is important). He then collapses
• Later, he takes out his switch blade, and stabs Dudley in the calf. He gets shot in the jaw.

Now, with all these in mind, it is fairly obvious that he died just then and there. But, epic reveal, HE'S ALIVE, with a few complications. Remember how Dudley used the same pistol on Jack Vincennes, and he died within a matter of seconds. Remember how he was also shot in the chest. So Bud's survival didn't make a whole lot of sense.

For your convenience, here's the original script, and it makes far less sense:

    At that instant, Dudley steps through the bathroom door.
    He's got Exley dead to rights.  As he squeezes the
    trigger, Bud leaps forward, pushes Exley hard to the
    ground.

    The SHOT passes through Bud's back by his left shoulder
    blade.  It spins him around.  A SECOND SHOT to the
    stomach slows him to a walk as he charges Dudley.  A
    THIRD ROUND SHATTERS Bud's jaw, but still he comes.
    Driven by rage, his hands reaching for Dudley's throat.
    He even gets hold before a FOURTH SLUG tears his chest.

So, if you have any ideas or explanations, please do let me know.

Here's the frame showing a bullet-hole on his right-lung. It's much clearer if you see the bullet-hole forming, and blood dripping out, than just a still shot. I added the red circle just in case.