Dogs don't 'nearly' bite people.
Seriously, dogs reactions are far far faster than our own, a dog that didn't land a bite, never intended to land that bite.
There are also a range of bites, and whilst 'teeth on skin' may constitute a bite in law, behaviourally that is not the whole picture.
There is the 'mouthing' very little pressure, but teeth on skin.
Muzzle punch - dogs mouth is closed or only partially open, lunges at you and hits with the front teeth.
Nip - front teeth only, varying levels of pressure possible
Bite and release - single bite, varying levels of pressure possible, then release
Multiple bites - dog repeatedly bites/releases/bites/releases - varying levels of pressure possible
Bite and hold - as it says.
Bite and rag - dog bites, holds and shakes his head
As far as pressure goes, theres the Dunbar Bite Scale which is the industry standard for determining the severity of a bite:
Level 1- Dog growls, lunges, snarls-no teeth touch skin. Mostly intimidation behaviour.
Level 2- Teeth touch skin but no puncture. May have red mark/minor bruise from dog’s head or snout, may have minor scratches from paws/nails. Minor surface abrasions acceptable.
Level 3- Punctures ½ the length of a canine tooth, one to four holes, single bite. No tearing or slashes. Victim not shaken side to side. Bruising.
Level 4- One to four holes from a single bite, one hole deeper than ½ the length of a canine tooth, typically contact/punctures from more than canines only. Black bruising, tears and/or slashing wounds. Dog clamped down and shook or slashed victim.
Level 5- Multiple bites at Level 4 or above. A concerted, repeated attack.
Level 6- Any bite resulting in death of a human
So im with the OP here, as a professional, this is not a vicious dog, this is a dog startled out of sleep by a silly human. I wouldn't allow this dog to sleep on a child or be where a child may startle them, I would expect an adult to remember not to be an idiot.