There's a big, big different between a dog who's bitten because:
someone cornered it
someone was breaking up a dog fight
it was fence reactive and someone reached through
or even bit a child because that child was in it's face
and rehoming a dog that's had various bites, and seems to become aggressive, even towards family members, for an unknown reason or with random, unpredictable triggers.
Not every dog that bites is "unstable" or "aggressive". And not every aggressive dog is unstable. Bamm is, even with family, unpredictably aggressive, or at least unpredictably triggered. Rehoming him to an unprofessional would, IMO, be highly irresponsible (as well as legally risky).
Sanctuaries can be good and bad, and some dogs are appropriate to place in a sanctuary environment, and some are not. Personally, if I was in Amber's shoes and decided Bamm was unsafe in the home, I do not think I'd place him in a sanctuary.
A lot of sanctuaries ARE capable of providing the exercise and stimulation most dogs need. We have one run by our local shelter where dogs that are too much of a bite risk to be adopted out live. They are frequently in kennels, but each day they have a chance to run around in large, fenced, wooded areas. They can play with other dogs if they enjoy that, and if they are capable, spend time in a home-like office. Some are quite bonded to the volunteers.
However, a dog that craves human attention, bonding, praise...would probably not do well there. I don't know how Bamm is socially when he's not anxious or having issues. I know my own dog would be horribly depressed if he didn't have his own family or person to live for, even with interaction and playtime and exercise and places to explore. A more independent dog could surely find joy in frolicking among the trees and being taught tricks for snacks or toys by a volunteer that they see a few times a week.