My Ops group runs 2 Op healers and 2 Sin tanks.
Over 50% of our in-combat rezzes are not battle rezzes.
It depends on group makeup obviously, and individual competence, but saying that anyone should automatically battle rezz is a little silly. It is always situational, and if there's any ambiguity whatsoever, the raid leader should make the final call (and live with the consequences).
Being in an organized raid group is very different from being in a pug - each raid group will look different and will thus have their own rules for it, and if you are in that raid group, you'll know about them, hence it's pointless to add exceptions for that - but the default behavior, if not told otherwise, should be to use that res.