I think your summary doesn't include the most interesting bit imho: the sign of the error is different (incompetent overestimate their competence, the competent underestimate).
I think that bias makes sense: if you have 0% competence it's hard to underestimate, and if you're at 100% competence it's hard to overestimate. So if we assume that they're truncated normal curves and translate them into a simple average, that's what we'll get.