From his Commentary on the Gospel of John X.27, copied from newadvent.org:
When He was raised from the dead, John 2:22 His disciples remembered that He spoke this, and they believed the Scripture and the word which Jesus had said.This tells us that after Jesus’ resurrection from the dead His disciples saw that what He had said about the temple had a higher application to His passion and His resurrection; they remembered that the words,In three days I will raise it up,pointed to the resurrection; believed the Scripture or the word which Jesus said, before. For faith in its full sense is the act of him who accepts with his whole soul what is professed at baptism. As for the higher sense, as we have already spoken of the resurrection from the dead of the whole body of the Lord, we have now to note that the disciples were put in mind by the fulfilment of the Scripture which when they were in life they had not fully understood; its meaning was now brought under their eyes and made quite clear to them, and they knew of what heavenly things it was the pattern and shadow. Then they believed the Scripture who formerly did not believe it, and believed the word of Jesus which, as the speaker means to convey, they had not believed before the resurrection. For how can any one be said in the full sense to believe the Scripture when he does not see in it the mind of the Holy Spirit, which God would have us to believe rather than the literal meaning? From this point of view we must say that none of those who walk according to the flesh believe the spiritual things of the law, of the very beginnings of which they have no conception. [Emphasis mine. Links in the text go to the Bible or Catholic Encyclopedia on NewAdvent.org.]
I think Origen here makes an important point about knowledge of scripture. Whether or not one acknowledges the divine origin of scripture, I think it is clear that there is a difference in understanding between the believer and one who does not. That doesn’t mean that those who don’t believe cannot understand the statements of scripture, but simply that there will always be a difference that it would be helpful for both to acknowledge.