Can a non-believer interpret God's Word accurately?

Based on the Word of God, e.g., Matthew 13: 10-16, a non-believer cannot consistently interpret the Scripture accurately. After Jesus had told the parable of the sower to large crowds (Matthew 13:2), His disciples asked Him why did He speak to those crowds in parables. Here is the passage from the NASB version:

¹⁰ And the disciples came and said to Him, “Why do You speak to them in parables?” ¹¹ Jesus answered them, “To you it has been granted to know the mysteries of the kingdom of heaven, but to them it has not been granted. ¹² For whoever has, to him more shall be given, and he will have an abundance; but whoever does not have, even what he has shall be taken away from him. ¹³ Therefore I speak to them in parables; because while seeing they do not see, and while hearing they do not hear, nor do they understand. ¹⁴ In their case the prophecy of Isaiah is being fulfilled, which says,

‘You will keep on hearing, but will not understand;
You will keep on seeing, but will not perceive;
¹⁵ For the heart of this people has become dull,
With their ears they scarcely hear,
And they have closed their eyes,
Otherwise they would see with their eyes,
Hear with their ears,
And understand with their heart and return,
And I would heal them.’

¹⁶ But blessed are your eyes, because they see; and your ears, because they hear.

Spiritual things are discerned spiritually. They do not make sense to unregenerated people. They need first to be born again (John 3:3,7). Without the new birth, they cannot understand the deep things of God in His Holy Scripture. The Lord Jesus let His disciples know that only those who believe in Him (are His disciples) will be able to discern His sayings. 

Sometimes, it may not be worth (in terms of energy, time, and resources) debating with atheists/agnostics when they are not on the same wavelength to begin with, e.g. Creation v/s Evolution (among others) debates. Unless the Holy Spirit of God makes a breakthrough Himself, the best sound intellectual argument would not change their pre-set minds. Repentance comes only through the power of the convicting Holy Spirit, not the flesh.