Interesting question...
I'm inclined to agree with
krupintupple. "Immunity to fear" isn't usually a special quality in the monster-entry sense (although it can be); it's more commonly derived from spells, creature type and class features. As the OP pointed out, immunity to fear in monsters is normally superseded by general immunity to mind-affecting effects.
Interestingly, there are a few spells and effects out there that have the [Fear] type - or otherwise cause the shaken, frightened or panicked states - but aren't listed as [Mind-Affecting]: for instance
touch of Vecna [Evil, Fear] and
blade of pain and fear [Evocation]. All of which is just to point out that there is precedent for non-mind-affecting fear, which perhaps prepares the ground a bit for creatures immune to mind-affecting effects to feel fear.
(Spell-like or supernatural fear
attacks - i.e. those part of a creature's entry - are all mind-affecting as per the slightly-redundant-sounding general description: "All fear attacks are mind-affecting fear effects.")
Sorry about the tangent there.
Anyway, I'm going with the ability overriding "immunity to mind-affecting", for the following reasons (absolutely none of which are RAW):
1) It's frickin'
cool. "I am just so badass I can frighten Vampires" is a great thing to be able to claim.
2) Immunity to mind-affecting conditions or not, everything that can do something remotely classifable as "thinking" is subject to fear. OK, it might not be subject to the
game effects of fear - shaken, frightened or panicked - but it can feel fear of one sort or another. Vampires fear sunlight, Paladins fear their loved ones having dreadful things happen to them and so on... They're just not usually
disabled by their fears, which in mechanical terms means "immune to fear". Vampires will still run from sunlight, Paladins won't dive into molten lava to follow the evil fire-creature unless they've got the right protective magic: a degree of fear is
necessary for most creatures and so it makes sense that an ability could exist that inflates the desire for self-preservation to a debilitating level. All Greater Mastery of Terror does is allow "fear" to have a game effect on creatures that it normally wouldn't bother. To me, it's pretty intuitive.
3) If it isn't read that way, it basically doesn't do a damn thing most of the time... except when NPC's use it. Player characters get immunity to fear from gods-know-how-many different spells: it's almost like "immunity to fear" is thrown in for free whenever a spell doesn't look like it does quite enough. A buffed mid-level party is likely to be immune to fear almost as an afterthought. As such, this ability is really useful for NPC's... but when you turn it around for PC use and look at the laundry list of monsters
specifically immune to fear, it's pretty damn small.
Nonetheless, if I were running a game where this was brought up, I would make an exception: creatures with no Intelligence score are still immune to fear, because I feel that to say otherwise is counter-intuitive. A Golem will, if so ordered by its master, throw itself into a volcano or saw its own legs off without hesitation and regardless of consequences... How can something like that be afraid? It's no more intelligent than a chair. Same with mindless undead: they're
mindless, which means they actually will follow something into a lake of fire or a pool of holy water if their standing orders mean they're supposed to follow it.
(Yeah, I know, but turning and rebuking are "special". I can feel the ice creaking under my feet, but I'm staying put

)
In the case of vermin, it's not so cut-and-dried but I'd probably stick with the "no Int, no scared" rule for the sake of simplicity. For some creatures, it makes sense that they could
potentially be frightened even if they're normally immune to the ill-effects of same. For others, it just flat-out doesn't compute to have them be afraid, regardless of what they're subjected to.