I ask myself when setting external consequences, "Is it related? Is it relevant? Is it reasonable? What will this teach him about said thing?"
I also look for other contributing factors. 6 years old are probably getting molars, so is he in pain? Also, if this was an unusual incident, I would want to know what precipitated it. For instance, if someone was trying to touch him inappropriately, I could be ok with biting.
I would talk about other ways to handle it, but I wouldn't be upset with the biting in that situation. If it was because someone took something, I would be more upset and see he needs more frustration tools.