My worst bites ever, both down to the bone, both requiring stitches were from a severe macaw and a shamrock macaw respectively.
The worst injuries I have seen were 2 macaws and a very, very friendly CAG who got spooked and displacement bit.
One was a macaw who was not well socialized, and the woman was repeatedly warned to get away from the bird and stop what she was doing because the bird was trying to go after the ring on her finger, that she was teasing him with...
Well, the bird got it! Had to remove her finger first though... the good news is that we put it on ice, and it was successfully surgically reattached.
The second was a love of a CAG who was just frightened by something, and unfortunately, he displacement bit. Twice as unfortunately, he was sitting on his owner's shoulder at the time. Went clean through her cheek, and the owner required facial reconstruction surgery... (I rehabbed that bird.)
The third was errily similar, an unsocialized macaw, overbonded to his person. DID NOT LIKE STRANGERS!!! WAS NOT BITE PRESSURE TRAINED!!!
The guy threw a party - something like 80 strangers in the house - and the bird went bonkers... So, in a brilliantly thought through move, the guy took the bird out of his cage, put it on his shoulder, and went back into the crowd of strangers. The first time a stranger brushed up against the bird's tail, he got mad and displacement bit, and split his face open from jawbone to lip. Again, facial reconstructive surgery. (I rehabbed that bird, too.)
My own sweet Sally bird, a Red Lored Amazon, got tired of her former owner beating her, and inflicted a severe degloving injury to her thumb. The lady took her to the vet to be destroyed, and that's how I got her... (Same bird now curls up into a ball and uses my cheek for a pillow, but she certainly did not come that way!)
Oh, and then there was a Scarlett that loved the husband and tried to drive the wife out of the nest. Got down on the floor and de-gloved a few of her toes...
My evil Dusky conure once got mad at me and put his beak clean through my finger, as in point coming out the other side...
I had a really funny escape artist lovebird let himself out of his cage and perch on my finger one day. He did his little happy bird dance, and when he finished dancing for me, he put about 6 holes in my finger!
SO ANY BIRD CAN...
Anything Amazon sized or larger has the power to inflict a de-gloving injury, or inflict a bite requiring stitches.
Anything in the U2, M2, and large Macaw size has the power to Amputate.
My greenwing can snap blocks in half that are thicker than my arm... So I always assumed she could go clean through that as well if she wanted to.
I watched a Hyacinth tear a "normal" macaw cage apart one day. Effortlessly popping cage welds. There's a reason they keep those guys in stainless...
The fact that more people don't get seriously injured is an indication that these guys don't intend to inflict injuries.