We've discussed this sort of thing before on this site and it really comes down to personality. I think that the advice in the column will be appropriate for some people, and inappropriate for others. This part in particular:
So say, "I'm sorry" or "This must really be hard for you" or "Can I bring you a pot roast?" Don't say, "You should hear what happened to me" or "Here's what I would do if I were you."
Different people receive comfort in different ways. When I'm needing comfort I don't want to hear, "This must be so hard for you" or similar phrases. They are not helpful at all.
ETA that I do agree that you should never make someone else's illness/tragedy about yourself. In that the article was spot on.