"as Pilate was satisfied that Christ had been accused through malice and envy. DA 729.1"
"For he knew that for envy they had delivered him."
The EGW passage directly reflects the principle stated in Matthew 27:18, that Pilate recognized Jesus was accused out of envy.
"Herod questioned Christ in many words, but throughout the Saviour maintained a profound silence. At the command of the king, the decrepit and maimed were then called in, and Christ was ordered to prove His claims by working a miracle. Men say that Thou canst heal the sick, said Herod. I am anxious to see that Thy widespread fame has not been belied. Jesus did not respond, and Herod still continued to urge: If Thou canst work miracles for others, work them now for Thine own good, and it will serve Thee a good purpose. Again he commanded, Show us a sign that Thou hast the power with which rumor hath accredited Thee. But Christ was as one who heard and saw not. The Son of God had taken upon Himself man's nature. He must do as man must do in like circumstances. Therefore He would not work a miracle to save Himself the pain and humiliation that man must endure when placed in a similar position. DA 729.2"
"And when Herod saw Jesus, he was exceeding glad: for he was desirous to see him of a long season, because he had heard many things of him; and he hoped to have seen some miracle done by him."
The EGW passage directly references and expands upon the account in Luke 23:8, specifically Herod's desire to see a miracle performed by Jesus.
"He saved others; himself he cannot save. If he be the King of Israel, let him now come down from the cross, and we will believe him."
Both passages deal with the idea of Jesus being challenged to perform a miracle to prove his power, and the taunt that he saved others but cannot save himself. While the context is different (Herod vs. the crowd at the crucifixion), the underlying theme is similar.