Think of it like armor. When you purchase it from a vendor it's common, when it's created by a profession it's uncommon. Some earned via questing and quest rewards and reputation (vendor) very between Uncommon and Rare. As of right now, I think they there isn't any intention of making profession pets proc a rare.
The battle stones, were pretty much created to counter the fact that Blizzard chose several pet rarity value which most of us considered a devaluation of something we might have wanted to play with, say like Legs from Children's week was Uncommon and can you imagine if you wanted to use only that pet and you were about to do the legendary dailies.
The main point if you purchase the pet, then the rarity of that pet can only be changed by the person purchasing it with the help of a Battle-Stone.