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A Large-sized creature that is innately Large (not through magic, but their race just normally being that big) is not under any effects that provide a Size bonus. Therefore, you can cast Enlarge Person on them to make them Huge, and gain all the bonuses and penalties related to that spell.
The size bonus on the Mammoth Rider PrC's animal companion is mostly just so that you don't have to cast animal growth on them to have them be big damn mounts. Furthermore, there are other classes that would consider going into Mammoth Rider, and some of those don't even get spells, so it's a definite advantage for them.
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The simplest way to explain it is that a Large-sized creature is that big because it naturally grew that big. It is not an over-sized Medium-sized creature. Spells and effects consider Large to be its base size, and increase it from there.
In the case of the Mammoth Rider, it increases the animal companion's size through a class feature , so it isn't naturally a Huge-sized creature. Therefore, Animal Growth overwrites the stat increase.
Another way of saying it would be that there is no such thing as non-magical Size bonuses. The bonus a large ogre gets to strength isn't a size bonus; it's part of being an ogre, the same way a medium orc gets a bonus to strength as part of being an orc.
AFAIK, the only way to obtain an actual Size bonus is through Polymorph spells(Either Enlarge/Reduce Person, or the X shape spells). These size bonuses never stack.
The only rule is that magical effects that increase size do not stack. In other words: spells, spell-like abilities, and supernatural abilities would not stack with each other, since they're all considered magical in some way (suppressed by anti-magic field, etc).
However, extraordinary effects are not considered magical, so size-increasing extraordinary effects would stack. This means an Eidolon's Large/Huge evolution would stack with an enlarging spell, since it is an extraordinary effect on an eidolon. On the other hand, a primal companion hunter's eidolon-mimicking ability, while it can still select Large/Huge, would not stack with enlarging spells, since it's typed as supernatural.
As to the mammoth rider, the huge-sized companion is extraordinary and would therefore stack with a size-increasing effect.
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In short, yes, because there is not really any such thing as a natural "size bonus". It is unfortunate that writers keep using "Size bonus" when they don't really mean a "bonus" as in something that can or can't stack with another bonus. But you can safely ignore the wording when dealing with the natural size of a creature.
So, racial creation rules have nothing to do with any bonuses. You shouldn't be reading racial or monster creation rules and trying to compare them to other rules. (Especially since they are largely "guidelines" more than rules.)
Large races don't get a "size bonus", those are merely the adjustments you make when increasing the size of your starting template. The new race is not walking around 24/7 with a "size bonus" to strength. It is just bigger and stronger than some other creature.
Same goes for when your Animal Companion grows up (usually around level 7) and becomes larger, whether it's a dog that grows from small to medium, or something else that grows from medium to large. They are not getting any size bonus, they are growing older and bigger.
You can still cast a polymorph or transutation spell on a Large creature, that increases its size, and it will grow to Huge and get a size bonus for growing. Not only that but you can gain size, enhancement, and inherent bonuses (if the AC can read a magic book that grants an inherent bonus).
So, it doesn't matter if it's worded "size bonus". Just ignore it. All of those are "racial" not "size", even though they say "size bonus".
Mammoth Rider's Gigantic Steed ability is an exception. I have seen it ruled both ways on the internet, this is because it is an Ex ability, not magical, and it is NOT just the natural growing up of the AC. Also it says "size bonus", just like all the above instances. Does the creature shrink if you abandon it? Even that is not known. But then it's a prestige class, which are often not as playtested and create confusion with broken rules. So I would treat it as an outlier case and not worry about it unless you want to create one.
If a polymorph spell is cast on a creature that is smaller than Small or larger than Medium, first adjust its ability scores to one of these two sizes using the following table before applying the bonuses granted by the polymorph spell.
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Hmm, that bit of the polymorph spells is a bit annoying.
My huge mammoth has a strength score of 32.
If I want to use a dire collar on it to make it gargantuan I'd actually lose strength instead of gaining it?
Huge adjusted to medium is -8, dire collar gives a +2. So I'm netting a -6 to strength because I'm enlarging?
Alternatively using the animal growth spell it would mean that the strength score wouldn't change (-8/+8) or even drop by 2 (the +2 size bonus from mammoth rider being overwritten by the +8 turning it into a +6 compared to normal)
Looks like I'm not going to bother with the dire collar or animal growth anymore, now that I know that I've been doing it wrong.
Damanta, the Dire Collar is not a polymorph effect, it is a size changing effect (as per Enlarge Person). Thus, you do not adjust the size to medium.