"They eagerly arrange to carry out their purpose; but Jesus sees what is on foot, and understands, as they cannot, what would be the result of such a movement. Even now the priests and rulers are hunting His life. They accuse Him of drawing the people away from them. Violence and insurrection would follow an effort to place Him on the throne, and the work of the spiritual kingdom would be hindered. Without delay the movement must be checked. Calling His disciples, Jesus bids them take the boat and return at once to Capernaum, leaving Him to dismiss the people. DA 378.2"
"When Jesus therefore perceived that they would come and take him by force, to make him a king, he departed again into a mountain himself alone."
Both passages describe the same event: Jesus withdrawing from the crowd who wanted to make him king by force. The EGW passage provides additional context and explanation for Jesus' actions, but it is clearly based on the biblical account.
"Never before had a command from Christ seemed so impossible of fulfillment. The disciples had long hoped for a popular movement to place Jesus on the throne; they could not endure the thought that all this enthusiasm should come to nothing. The multitudes that were assembling to keep the Passover were anxious to see the new prophet. To His followers this seemed the golden opportunity to establish their beloved Master on the throne of Israel. In the glow of this new ambition it was hard for them to go away by themselves, and leave Jesus alone upon that desolate shore. They protested against the arrangement; but Jesus now spoke with an authority He had never before assumed toward them. They knew that further opposition on their part would be useless, and in silence they turned toward the sea. DA 378.3"
"When Jesus therefore perceived that they would come and take him by force, to make him a king, he departed again into a mountain himself alone."
This passage directly relates to the same event as John 6:15, providing additional details about the disciples' perspective and motivations. It expands on the biblical account by explaining why the disciples were reluctant to leave and highlighting the potential for violence and insurrection.
"Jesus now commands the multitude to disperse; and His manner is so decisive that they dare not disobey. The words of praise and exaltation die on their lips. In the very act of advancing to seize Him their steps are stayed, and the glad, eager look fades from their countenances. In that throng are men of strong mind and firm determination; but the kingly bearing of Jesus, and His few quiet words of command, quell the tumult, and frustrate their designs. They recognize in Him a power above all earthly authority, and without a question they submit. DA 378.4"
"When Jesus therefore perceived that they would come and take him by force, to make him a king, he departed again into a mountain himself alone."
The EGW passage directly describes the event in John 6:15, elaborating on the reaction of the crowd and Jesus's authoritative manner. It's more than a thematic parallel; it's a retelling with added detail.