I had to observe that in most encounters “Elephant”, if used by a unit controlled by the player in the very first round of a battle, will not induce the shaken condition – even if the enemies save failed. In subsequent rounds there were no such problems. The A.I. controlled barbarians didn’t share this problem of the “first round”.
A few pictures:
in most encounters, but not all:
Also, the Psionic Beetle seems to be immune against the shaken condition, even if I don’t find any indications for this under “feats” or “effects”.