I agree in part. You could read Epictetus as saying "just try not caring about people," which I think is the incorrect reading. Instead, I think he's saying something like "take a step back and realize that your deep personal attachments don't look so important when you step outside your perspective. You can use this realization to help get past the deep emotional pain that is normal for people to feel."
However, the line about other's indifference I think can only be read as dark funny to a modern reader:
> has someone else's child or wife died? There's no one who wouldn't say 'So it goes.'