When our dog bit our son, we had to report it to the county. We were told to just quarantine our dog and wait a week to make sure he wasn't rabid. Not a big deal really.
That dog was put down shortly there after. I can't abide a biter, even if it's just a one time thing. Pets are supposed to enhance your life, not make it a pain in the ass.
Without knowing the full background, that sounds a little bit extreme. If I went off of your rule, then I would have to had put my dog down 3 years ago, last year, and back in January as he bit me each time. Each time was when I got home extremely late and opened the front door without saying anything to him. He was simply doing his job at protecting the house. And yes each time drew blood and left a scare. But oh well for me, the dog did what he was trained to do so I cannot fault him there.
I guess my parents would had to put down our yellow lab years ago as well since he bit my brother in the face after my brother bit the dogs ears ( he was 4...).