It is a good idea to watch body language and not get too distracted by the "am I looking it in the eye" thing. Body language can tell you much more than eye color. But, dominant male gorillas are certainly not a wild animal you want to have a staring contest with. If it sometimes applies to bears as well, that doesn't surprise me, but I doubt it is as direct a statement of challenge with bears as it is with dominant male gorillas, whom we are much more closely related to.
They say the same thing of any animal threat including human, so I can't say it is true of bears in particular, whereas dominant male gorillas...