I would stipulate that it doesn't really matter if he can or not. It's nice if children understand the rationale behind parental authority, but it's not essential. What is essential is their obedience.
And yes, I think that many, many individuals are incapable of understanding the Word of God correctly. Your theology seems to leave a big hole for children, the mentally ill, the ignorant, the illiterate, and the slow-witted. Those folks all have to trust that *someone* in authority is giving them the straight dope on the Gospel--their parents, pastor Bob, First Baptist Congregation, etc. And I would submit that the 2000 year Magisterial teaching of the Universal Church is far more deserving of obedience than any of those.
More deserving than the Bible.