You get one attack roll for each natural attack you possess, and you do not get any extra natural attack for high BAB (you still gain extra weapon attacks for high BAB if you are using a weapon)
In the case of the Oliphant exposed, because both the Gore and Stamp attacks are primary, you get all the three attacks at your full BAB, and no extra attack because of a high BAB. Assuming your size is Huge:
Melee gore +11 (2d8+5), 2 stamps +11 (2d6+5)
Bonus break down: +8 BAB +5 Str -2 size (because all the three attacks are of primary type, the -5 penalty to secondary attacks does not apply)
The confusion happens because the no BAB extra natural attacks is not clearly stated in the monster rules natural attacks entry, but it is specified in the combat chapter in the natural attacks entry under the Attack section as referenced in the question.
For a full explanation about BAB and natural attacks, first of all, the rule which states you get extra attacks as your Base Bonus Attack (BAB) rises is under common terms definition:
Base Attack Bonus (BAB): Each creature has a base attack bonus and it represents its skill in combat. As a character gains levels or Hit Dice, his base attack bonus improves. When a creature's base attack bonus reaches +6, +11, or +16, he receives an additional attack in combat when he takes a full-attack action (which is one type of full-round action—see Combat).
So by the BAB rule you get additional attacks when you reach certain BAB levels.
Let's check what the natural attacks rules say:
Natural Attacks: Most creatures possess one or more natural attacks (attacks made without a weapon). These attacks fall into one of two categories, primary and secondary attacks. Primary attacks are made using the creature's full base attack bonus and add the creature's full Strength bonus on damage rolls. Secondary attacks are made using the creature's base attack bonus –5 and add only 1/2 the creature's Strength bonus on damage rolls. [...]
Creatures with natural attacks and attacks made with weapons can use both as part of a full attack action (although often a creature must forgo one natural attack for each weapon clutched in that limb, be it a claw, tentacle, or slam). Such creatures attack with their weapons normally but treat all of their natural attacks as secondary attacks during that attack, regardless of the attack's original type.
So nowhere says natural attacks do not get extra attacks for high BAB, but it neither says they do, and it makes a clear difference between natural attacks and attacks made with weapons. So the intention seems clear that natural and weapon attacks are different things and work differently.
The confusion is cleared when you check the natural attacks entry of the Combat section:
You do not receive additional natural attacks for a high base attack bonus.
We can also infer this works like that from examples. In this case take a look to the Bear in Paizo Bestiary. At one side we have the Grizzly Bear (BAB +3) at the other the Dire Bear (BAB +7):
Bear, Grizzly:
Melee 2 claws +7 (1d6+5 plus grab), bite +7 (1d6+5)
Base Atk +3; CMB +9 (+13 grapple); CMD 20 (24 vs. trip)
Bear, Dire:
Melee 2 claws +13 (1d6+7 plus grab), bite +13 (1d8+7)
Base Atk +7; CMB +15 (+19 grapple); CMD 26 (30 vs. trip)
As you can see the Dire Bear has +7 BAB, which corresponds to an attack iteration of +7/+2, but if you look at the Dire Bear attacks, he has exactly the same number and type of attacks than Grizzly bears. Thus, it seems that Pathfinder developers intention is high BAB does not give you access to additional natural attacks, and that is something reserved to weapon attacks, unnarmed strikes and combat maneveurs.
Remember you need to take a full-attack action in order to perform all your natural attacks, and you still benefit from additional attacks if you are holding at least one weapon.
Addendum about natural attack bonuses
When performing multiple natural attacks, you have also to take into account the difference between primary and secondary attacks. So let's see when a natural attack is considered primary or secundary based on the universal monster rules:
Primary: You attack with full BAB and full Strength damage bonus. Are considered primary:
- Typical primary natural attacks: Bite, Claw, Gore, Slam, Sting, Talons
- Whatever attack if it is the only type of natural attack the creature has (be it single attack as a Tile Slap, or multiple as 2 Pincers)
Secondary: You attack with BAB -5 and half Strengh damage bonus. The multiattack feat reduces this penalty from -5 to -2. Are considered secondary:
- Typical secondary natural attacks: Hoof, Tentacle, Wing, Pincers, Tail Slap, Others...
- Whatever attack if it is used in combination with weapon attacks (including unarmed strikes).
Five: Three with one Claw, once with the other, once with the Tail
Improved Rapidstrike means that you get two extra attacks with one of your claws, and you still get your other claw attack and the tail attack (which are not affected by Rapidstrike), up to a maximum of five attacks.
Your attack routine, assuming +15 BAB (minimum for Imp. Rapidstrike) and 1d6 damage on each natural weapon, would be as follows:
+15/+11/+6 Claw (1d6+Str), +15 Claw (1d6+Str), +15 Tail (1d6+½Str)
The extra attacks granted by Improved Rapidstrike are not secondary attacks so they are not affected by Improved Multiattack. A pair of natural weapons can both be primary, so the second Claw attack isn’t affected either. Imp. Multiattack does affect the Tail attack, which is secondary; without it it would be at −5 or −2 with Multiattack.
Personally, without more secondary attacks, I wouldn’t spend the feats on Multiattack and Improved Multiattack. Even with a few more secondaries, I usually find Multiattack to be enough.
Best Answer
There's a GM ruling to be had here, depending on the order they choose to apply effects. At my table, Yes, the creature can take and benefit from the feat, depending on the circumstances.
Taking the feat: The prerequisites are pretty straightforward. It's fairly clear you can take the feat if you have at least three natural attacks.
Benefiting from the feat: This is a little harder, and where the GM call comes in, but here is what I consider the "common sense" call. Normally, a creature with only primary natural attacks doesn't gain any benefit from Multiattack because they have no secondary natural attacks to reduce the penalty on. However, many creatures are intelligent enough to use weapons. When you make a full attack with one or more manufactured weapons, you can still add each of your natural weapons (except usually claw or slam attacks that use the hand you're holding the weapon in) to that full attack in addition to getting your full complement of normal attacks, but those natural attacks are treated as secondary attacks regardless of their normal status.
Your example creatures with two claws, a bite, and a gore could still use the bite and gore (and possibly a claw) while taking a full attack with a weapon. Depending on his BAB, he might be able to take multiple attacks with a weapon or two and still get in two or three of his naturals as well. In these cases, the Multiattack feat will offset three points of penalty to each natural weapon attack, changing them from -5 to -2. If the damage difference between his claws and his weapons is significant, this can be a very advantageous move.
Two other uses for using weapons in addition to natural attacks: reach weapons and ranged weapons. Using a longspear can double your reach, while allowing you to retain the ability to attack and threaten the adjacent squares as well, thanks to your bite and gore attacks. An archer or crossbowman could still make two attacks into his melee range as part of a bow full attack, and still threaten melee as well. Just note that your ranged attacks still provoke attacks of opportunity.