When my now teenage daughters were younger, my youngest daughter, then 3, hit my collie in the back of the head with a piece of 2"x4". Did she get bit? No. Did she deserve to? You bet. Her mom spanked her butt good.
Yes, a three year old can provoke a bite.
And before you jump on me for taking the dogs side, 18 months ago I had a beautiful male rottweiler put to sleep for biting my then 4 year old son. It was an unprovoked bite.
There is a difference. And they should be treated differently.