This isn't about helping the other friend. It's about HER need to be in charge, to be validated in her own mind by having all the info. It's most likely the reason why the other friend shared with you and not with her.
In the future, you might just give out less information - not even letting someone know that you know the whole story. Not that you did anything wrong, but it avoids the situation you are now in. Some people who can't handle it sort of view people like you as being "privileged" or even "showing off" - not that you are, just that they view it that way. And you might be able to avoid this sort of confrontation.
If anything, you can say "Sorry you feel this way. It's not my information to share, not my story." Or say nothing - it's unlikely that you're going to get too far if she says "I'm done with you." Very immature. As Elayne says below, she has shown you who she is. Believe her.
There's a reason this friend-on-the-rocks didn't ask the other friend with the original problem, isn't there? She knows she's not been chosen as the repository for the details. And the reason is probably that her need to know is far greater than the other woman's need to share.
You sound like a good friend - be happy with that.