Be suspicious of people who you don't know that well, but all of the sudden they pop up in a moment of crisis. Sometimes they want to be part of it and go around and brag to others how their friend / relative is suffering. It's just a source of gossip for them. Then they get the sympathy-by-proxy and they get others to pity them and so on.
As a general rule I find that people who want to celebrate with you when something good happens and are happy for you are more likely to be a better friend than the ones who show up when you're in trouble.
> "Can I bring you a pot roast?"
Also don't say "what can I do to help?". People as a rule will just say, "Sure, thank you" but the understanding is you're not serious and you just said it because you're expected to say. You might have meant it, but they don't know that. Like the article mentions, say something like "Would you like a pot roast?".