Technically you are correct, in that there is not consensus on the origins of the owlbear, but having read it's entries over multiple editions, you start to get an idea that this is a large destructive non-native predator. And as someone who lives in a country with wildlife that has been horribly affected by the introduction of non-native apex predators, I absolutely advocate for the culling of destructive non-native predators.
From the AD&D Monster Manual, it has no type classification in this book:
The horrible owlbear is probably the result of genetic experimentation by some insane wizard. These creatures inhabit the tangled forest regions of every temperate clime, as well as subterranean labyrinths. They are ravenous eaters, aggressive hunters, and evil tempered at all times. They attack prey on sight and will fight to the death.
From the 3e Monster Manual, it is classified as a beast in this book:
Owlbears are extraordinarily vicious predators with a reputation for ferocity, aggression, and sheer ill temper. They tend to attack nearly anything that moves without provocation. Scholars have long debated the exact origins of this creature. The most common theory is that a demented wizard created the first specimen by crossing a giant owl with a bear.
The 3.5 monster manual entry has the same lore text, but it has been reclassified as a magical beast.
From the 4e monster manual, it has been reclassified again as a fey beast:
Infamous for its bad temper, an owlbear attacks anything it thinks it can kill.
A character knows the following information with a successful Nature check.
DC 15: Owlbears are dangerous predators of the Feywild that made their way to the natural world long ago. They typically lair in forests and shallow caves. They can be active during the day or night, depending on the habits of the available prey. Adults live in mated pairs and hunt in packs, leaving their young in the lair.
And the 5e monster manual, which easily has the largest lore text (I will copy the relevant parts), and has reclassified it as a monstrosity:
Deadly Ferocity. The owlbear's reputation for ferocity, aggression, stubbornness. and sheer ill temper makes it one of the most feared predators of the wild. There is little, if anything, that a hungry owlbear fears. Even monsters that outmatch an owlbear in size and strength avoid tangling with it, for this creature cares nothing about a foe's superior strength as it attacks without provocation.
Savage Companions. Although they are more intelligent than most animals, owlbears are difficult to tame. However, with enough time, food, and luck, an intelligent creature can train an owlbear to recognize it as a master, making it an unflinching guard or a fast and hardy mount. People of remote frontier settlements have even succeeded at racing owlbears, but spectators bet as often on which owl bear will attack its handler as they do on which will reach the finish line first.
Elven communities encourage owlbears to den beneath their treetop villages, using the beasts as a natural defense during the night. Hobgoblins favor owlbears as war beasts, and hill giants and frost giants sometimes keep owl bears as pets. A starved owlbear might show up in a gladiatorial arena, ruthlessly eviscerating and devouring its foes before a bloodthirsty audience.
Owlbear Origins. Scholars have long debated the origins of the owl bear. The most common theory is that a demented wizard created the first specimen by crossing a giant owl with a bear. However, venerable elves claim to have known these creatures for thousands of years, and some fey insist that owl bears have always existed in the Feywild.
