However I don't believe the broomstick or severed finger stuff.
It's not a myth. They can, and I have seen it happen! Those blocks of hardwood they snap are harder and denser than bone.
Lawsuit Dad sues when hotel bird amputates his son's finger:
Dad Sues Over Trauma of Seeing Parrot Attack Toddler | Animals
Doctor who specializes in finger wound treatments, and has done surgical reattachments from Macaw bites. Includes pictures of a person who almost lost a thumb to a B&G (bitten through, but not quite off!)
Infections and bite wounds | The Hand Treatment Center - New Jersey/New York Hand Surgeon
They usually won't unless provoked to the extreme... and even then it's usually no more than a puncture wound and/or bruise requiring a band aid. Hurts, but not serious. Most bites requiring stitches are due to the bird not realizing its own strength, and applying too much pressure. And to me, macaws are the easiest of the bunch to bite pressure train. I very nearly lost the tip of my right index finger to a friendly macaw who didn't realize his own strength. He was just holding on for dear life, not wanting me to walk away. My left thumb was also sliced open to the bone - by a MINI-MAC! And that was just a quick "GOTCHA SUCKER!" bite. He didn't really get a chance to clamp down all the way, it was a slice and retreat bite...
Aside from the aforementioned military macaw "getting the ring" off the finger (easy! first remove the finger. The ring slides right off!), a friend of mine had a scarlet macaw that inflicted a severe degloving injury to three toes, and years ago I did a rescue on a macaw "beak through the cheek" which required surgical repair... Maggie is SIGNIFICANTLY larger and more powerful than either of those birds. (She also wouldn't hurt a fly... it is simply not in her nature.)
The worst bite injury I'm aware of, however, was from a displacement bite by a CAG. (Beak through the cheek, with the bird then knocked off the owner's shoulder, with the beak still caught in the cheek. Yikes!) That lady required facial reconstructive surgery. (I rehabed that bird! He was tame and sweet. He was a displacement biter who just got spooked out of his mind...)