First, I want to remain mindful of the underlying tragedy. This is going to sound like I'm reducing it to a clinical explanation and that's not my intent. My heart breaks for this family.
It depends on how quickly the individual is removed from the environment. The one person I met who it happened to was a U.S. Navy diver who had stuck his head up inside a saturation bell that was full of helium due to an undiscovered gas leak. He took one breath and basically self-rescued by passing out and falling back through the bell hatch into fresh air. The only thing he got was a nasty bump on his head. The probability of survival goes down very quickly the longer the individual is exposed though - much more quickly than someone who has gone into respiratory arrest from (for example) a drug overdose and is simply deprived of oxygen. Pure helium (or any other pure gas that isn't oxygen, as
@Wookie pointed out) will act like an oxygen vacuum because of the large diffusion gradient between the bloodstream and the lungs. This results in extremely rapid hypoxemia, which would lead quickly to irreversible tissue damage. So, minute for minute, it would be much more difficult to resuscitate someone who had breathed pure helium, and that's on dry land. In the water, an unconscious individual would drown quickly.
<edit> I was typing this as
@mderrick was typing his well-considered post above - same idea, different wording.