Having a lot of confidence in your abilities is arguably a pretty important quality in an employee. I've encountered a lot of engineers who were way less effective than they could have been, mainly because they were too timid to speak up, to take initiative, to lead.

So maybe they were right to reject someone who answered 4-6 in most categories. Either that person isn't a good fit skill-wise, or they are a good fit skill-wise, but not personality-wise.