"David was cordially received by the king of the Philistines. The warmth of this reception was partly due to the fact that the king admired him and partly to the fact that it was flattering to his vanity to have a Hebrew seek his protection. David felt secure from betrayal in the dominions of Achish. He brought his family, his household, and his possessions, as did also his men; and to all appearance he had come to settle permanently in the land of Philistia. All this was gratifying to Achish, who promised to protect the fugitive Israelites. PP 673.1"
"And David said unto Achish, If I have now found grace in thine eyes, let them give me a place in some town in the country, that I may dwell there: for why should thy servant dwell in the royal city with thee?"
The EGW passage directly recounts and expands upon the events described in 1 Samuel 27:5, providing additional context and interpretation of Achish's motivations.
"While dwelling in this isolated town David made war upon the Geshurites, the Gezrites, and the Amalekites, and he left none alive to bring tidings to Gath. When he returned from battle he gave Achish to understand that he had been warring against those of his own nation, the men of Judah. By this dissembling he was the means of strengthening the hand of the Philistines; for the king said, “He hath made his people Israel utterly to abhor him; therefore he shall be my servant forever.” David knew that it was the will of God that those heathen tribes should be destroyed, and he knew that he was appointed to do this work; but he was not walking in the counsel of God when he practiced deception. PP 673.3"
"And David and his men went up, and invaded the Geshurites, and the Gezrites, and the Amalekites: for those nations were of old the inhabitants of the land, as thou goest to Shur, even unto the land of Egypt. And David smote the land, and left neither man nor woman alive, and took away the sheep, and the oxen, and the asses, and the camels, and the apparel, and returned, and came to Achish. And Achish said, Whither have ye made a road to day? And David said, Against the south of Judah, and against the south of the Jerahmeelites, and against the south of the Kenites. And David saved neither man nor woman alive, to bring tidings to Gath, saying, Lest they should tell on us, saying, So did David, and so will be his manner all the while he dwelleth in the country of the Philistines. And Achish believed David, saying, He hath made his people Israel utterly to abhor him; therefore he shall be my servant for ever."
The EGW passage directly references and interprets the events described in 1 Samuel 27:8-12, including David's raids, his deception of Achish, and Achish's resulting trust in David.