In second grade for certain science lessons two classes would combine to see demonstrations of science experiments. One I remember clearly was that salt or sugar looking like crystalline rocks would disove in water and pass through a handkerchief. Out of two combined classes I was the only one who admitted not believing that so I was called to the front of the combined classes to help with and watch the experiment first hand. Yes, I had to see for myself that what was said was real. Through my life there have been things my mind has been focused on and so I question more than others in many things. A most recent instance is meeting people and making friends, especially via long distance communication.
Before I met my wife (long distance communication writing letters) there were several wrong choices I had made and mostly because I wasn't cautious. Since my wife passed I have several friends warn me about meeting someone from the start through long distance communication. One warning was "if it's to good to be true, it probably isn't true". So yes, I started cautious communication with a woman who from the start sounded quite right. But what stuck in my head and heart was what I had been told, look for certain signs. Beside research I did to learn more the overall convincing truth was this woman's love for the Lord. That can't be hidden, faked maybe, but even here the consistency continued to be quite real. She is a genuine godly woman.
So when I ask of a psalm, "Could Jesus have prayed this as a prayer?", familiar psalms still require certain elements which must be present to make the possibility quite real. As I come to familiar psalms they may require a deeper look beyond the familiar so once again I read the longest recorded prayer of Jesus, John 17. Much like the first verses of Psalm 19 Jesus begins His prayer speaking of the glory of God. As a man Jesus was able to see as we see when challenged with the heavens declaring the glory of God. But in His prayer Jesus speaks of the glory He had with the Father BEFORE the world was. Elsewhere in the Bible we have been told that eye has not seen, not ear heard of those wonders that lie ahead being with the Father. It is because of this point that Jesus may have been like the Jewish elders who had seen the original temple and then after more than seventy years seeing the rebuilt temple weeping because its glory was not quite the same as the original temple. The heavens declaring the glory of God definitely would have a different meaning to Jesus remembering the glory with the Father before the world was. But on the other side as a prayer Jesus praying could honestly verify in prayer that as a man the heavens and earth declare the glory ofGod the Father.
The truths of the action of God's Word found following verses Jesus could verify as well. Where someone might question Jesus praying this psalm is toward the end with simply stated concerns about faults and presumptuous sins. But looking closer:
Who can understand his faults? cleanse me from secret faults. Keep thy servant also from presumptuous sins: let them not reign over me: so shall I be upright, and made clean from much wickedness.
Psalms 19:12 - 13 GNV
As a man Jesus could have prayed these words and meant them. After all like us it is tests that reveal faults and the Word says that He was tested, tempted in all points as we are and yet without sin. So yes, there is a very real possibility that Jesus could have honestly prayed Psalm 19 as a quite real honest prayer.