A slightly different perspective:
But He was in all points tempted like as we are, yet without sin
Who among us has resisted unto blood, striving against sin? If it had been impossible for the Son of Man to sin, then it would have been impossible to tempt Him also. Why would He have needed to resist temptation so hard that He sweat great drops of blood, with an angel needed to strengthen Him (that certainly indicates the commission of sin was possible). Had sin been in an impossibility as He was the Son of Man, why would He have to resist it so hard.
Luke 22: 41-44 And he was withdrawn from them about a stone's cast, and kneeled down, and prayed, Saying, Father, if thou be willing, remove this cup from me: nevertheless not my will, but thine, be done. And there appeared an angel unto him from heaven, strengthening him. And being in an agony he prayed more earnestly: and his sweat was as it were great drops of blood falling down to the ground.
This is why:
For the Father judgeth no man, but has committed all Judgment to the Son, giving Him authority to execute Judgment because He is the Son of Man.
The entire exercise would be moot if it had been impossible for Him to sin.
In regards to a sin nature: Adam was created as a complete man (3:1) yet he was tempted and sinned. Lucifer was created by God as perfect in his ways until iniquity was found in him.
It is obvious that the commission of sin has never been relegated to a "sin nature". Neither Lucifer nor Adam had a "sin nature". Yet the Lord refers to Lucifer as the father of lies. God created all His angels and all people with their own absolute free will. Logically then with His creatures having their own hearts and minds, the possibility of their wills not matching His Will has always been present (anything not of faith is sin).
Please don't get me wrong, I am not pretending to understand the science of how the Word became flesh as God and Man but I do strongly believe They did it in a way in which final Righteous Judgment would be dealt out to both the Just and the unjust.