The spell animate dead usually applies to the targeted corpse the template skeleton or the template zombie

There's probably not going to be any direct developer support for or against your GM's ruling, likely because the developers considered the actual rules so obvious there was no reason to make such a ruling.

The spell animate dead targets one or more corpses, not specifically humanoid corpses and not mandating the resultant creatures be, for example, humanoid skeletons. Further,

• A zombie can be created only from a mostly intact corpse.
• A skeleton can be created only from a mostly intact corpse or skeleton.

The spell says nothing about transforming a corpse from the corpse of the original creature into the corpse of a humanoid. The template skeleton provides several examples of nonhuman skeletons, and the template zombie does the same. Seriously, all evidence points to, for example, a mostly intact 9 Hit Die green dragon corpse becoming either a 9 Hit Die green dragon skeleton or a 9 Hit Die green dragon zombie when such a corpse is the target of the spell animate dead (and requiring the expenditure of 225 gp of onyx as material components).

So, while it's hilarious to imagine, for example, a wizard casting the spell animate dead on the mostly intact skeleton of a vicious advanced megaraptor and ending up not with an advanced megaraptor skeleton but a 1 Hit Die humanoid skeleton, or a wizard casting the spell animate dead on the mostly intact corpse of a crocodile and ending up not with a zombie crocodile but a generic humanoid zombie, that's also deeply weird.

By the way, prior to this question, I'd never considered any other way of interpreting the spell animate dead except to animate monster corpses as monster corpses, but, as evidenced by this 2010 EN World thread, at least one other GM uses a similar house rule to your GM's house rule. (Or maybe that question's also about your GM's animate dead house rule? [Cue dramatic music.])

Working around these limits anyway

However, even if the GM insists that the spell animate dead when used to make skeletons or zombies only creates 1 Hit Die humanoid skeletons or zombies, options remain. The spell animate dead can turn a big ol' pile of those 1 Hit Die humanoid skeletons or zombies into a necrocraft, or the spell can make an isitoq or a beheaded. It will be difficult for the GM to argue against these alternatives given such creatures' descriptions' increased specificity.

These alternatives are just samples. The more bestiaries available, the more options multiply.

Yes, it is possible

It is actually possible to obtain a permanent skeleton companion. That being said, it is a slightly convoluted process that is not without certain shortcomings. This method involves using two spells in conjunction:

Finger of Death

A humanoid killed by this spell rises at the start of your next turn as a zombie that is permanently under your command, following your verbal orders to the best of its ability.

True Polymorph

Choose one creature or nonmagical object that you can see within range. You transform that creature into a different creature ... If you concentrate on this spell for the full duration, the transformation becomes permanent. ... If you turn a creature into another kind of creature, the new form can be any kind you choose whose challenge rating is equal to or less than the target's. The target's game statistics, including mental ability scores, are replaced by the statistics of the new form. It retains its alignment and personality. ...

By now, you probably understand where I'm going with this. You would first start by using Finger of Death to create a normal zombie servant under your control. Next, you would use the True Polymorph spell to transform said zombie into a skeleton (which you can do because they are both challenge rating 1/4). Then you simply wait out the spell's duration, which makes the transformation permanent, and, since a transformed creature "retains its alignment and personality" you now have one permanent skeleton companion at your disposal.

In fact, using this method, you could create a permanent companion out of any creature of 1/4 challenge rating you may desire.

In Summary

Finger of Death + True Polymorph = permanent skeleton companion