I was randomly exploring, went into this random cave, cleared it out, found the boss chest and what do I find inside? A Dragon Armour. I can't for the life of me remember which cave it was.

It doesn't seem to be a quest item, I can drop it around just fine.

Is it meant to appear this early? I'm only level 22. Is it even meant to appear in chests, ever? Or is this just a case of the random number generator going crazy?

I think you've just been incredibly lucky. According to UESP the base level it should start appearing at is 40 for Dragonplate and 46 for Dragonscale, but it can in rare circumstances appear at lower levels (doesn't say in what circumstances and says up to 12 levels earlier which you've beaten by a far bit) and like Daedric is 20 times rarer than other armours.

Seems like broken coding to me. I would think it would make more sense - from a design perspective - to make it have 0% chance of appearing at levels below 40, if that indeed was the intended level it should start appearing...

Oh well. I'm not going to use it yet anyway since it's still too early; it's currently put into storage. When the time is right (and when I can smith a full set) then I will put it to use...

I think they were trying to avoid the overly predictable loot-scaling that appeared in Oblivion. It does produce a few quirky results although its possible you just had some sort of glitch occur.

i dont think its bad coding, i found a daedric sword at level 4 in shimmermist grotto.

I found an ebony bow in a chest at level 8, come to think of it it may have been shimmermist grotto, as well.

I think certain chests have "Threat modifiers" that effectively multiplies the level of the player when generating loot, based on the perceived difficulty of the dungeon. This may be able to work as penalty as well as boon.