Why are some addictions healthy, and others not?

If I can be serious for a moment...

I recently volunteered for an organization that promoted healthy living for children.  I won't name them, as my experience with the organization was ultimately not a good one but overall I still support them (and my situation was unique, as many of you likely already know).  As part of my orientation, we watched a brief motivational speech given by the founder of the organization, someone who was an alcoholic until one day they woke up, decided enough was enough, and became an athlete.

It was quite obvious to me looking at this frail, emaciated several time Ironman that this person had traded in one addiction (alcohol) for another (running).  And yet person after person at the training gushed on about how inspirational this story was.

My serious question is, why was this inspirational?  Why is an addiction to running considered healthy and admirable, when other addictions are seen as character flaws?  Is there a point at which you are exercising too much?  People who exercise a lot, and I've been guilty of this at times, get aggressively defensive when accused of exercising too much.  It's easy to fall back on the "S/he's just jealous of me!" argument to dismiss your critics for not making exercise the same priority that you do.

But what about situations when someone actually is exercising too much?  One (very mainstream) web forum I was browsing the other day featured several threads talking about the Female Athlete Triad (and how ironic is it that its acronym is FAT) as though it were an ordinary, everyday thing - with amenorrhea maybe even as an indication that you were on the right track with your exercising.

It's an ambiguous idea.  I don't know the person that I'm criticizing above, even though they represent an archetype I've seen before.  That said, it seems clear that this person is not treating the root of their problems, namely their addictive personality.  On the other hand, if someone were to tell me, for instance, that I read too much, I promise you I would get defensive.