I was thinking, while I was raking leaves, that part of the weirdness with this could be caused by the a lack of clarity in or the misunderstanding of the game terms used. "Good" and "Evil" in the alignments are probably the best examples, but in this case it's "Fear."
Fear is a normal part of being alive. Anyone who has no fear is not somehow superior but somehow mentally defective. Seriously, that would be a real problem. Fear is required for bravery, since you aren't being brave if you do something you aren't afraid of doing. Bravery is a key characteristic of many D&D adventurers, especially Paladins, the classic archetype of the brave knight in shining armor. Of course, Paladins are Immune to Fear, which is where the lack of clarity starts. I would say that it's not so much that Paladins are Immune to Fear but that they are Immune to Panic. In other words, they are afraid, since fear is normal, but their fear doesn't overwhelm them and they're able to stand up and face their fears, secure in their faith or whatever, without running off whimpering.
In the case of Intimidation against any character, where being Intimidating is defined as attempting to make someone's fear overwhelm them, a target character might be afraid of whoever is Intimidating or whatever they say or do but won't necessarily "panic" and be Intimidated. So there would be fear but not D&D Fear, and a character might be afraid of that half giant or huge axe but won't just cave in to that fear.
Stupid language. Y'know, as many synonyms as there are for any particular concept, you'd think maybe we'd have each one mean something slightly different so we could have a very detailed and accurate way to express things.