Choosing to take damage to keep a card?

I'm aware that for cards with effects that require damage to be dealt to stay in effect require at least one HP to be loss to get the benefit and keep the card (unless it's destroyed some other way).

If Fanatic put Chastise on a legal target, and then Wagner Mars Base's Meteor Storm is played (all targets are immune to damage), can Fanatic choose to deal herself 1 psychic damage even though she (and all other targets) to keep Chastise, or will Chastise have to bestroyed because Meteor Storm is preventing all damage?

I assume that Chastise must be destoryed, but I was curious what the right/proper rule is. I was in this situation and played with Chastise being destroyed.

You cannot choose to take damage if you are immune, and Chastise will be destoyed.

Chastise would be destroyed since Fanatic is unable to deal herself any damage.

An exception to this is stuff like Wraith's Stun Bolt and Nightmist's Investigation. Since the secondary effects of reduce damage by 1 and draw 2 cards are not inherent on damage being done, even with something like Meteor Storm out, you could still have the secondary effect of both powers.

Cool, that's what I thought. I think the game is more interesting that way.