"believed that the troops of Saul would not be ordered to invade this sacred place, but no place seemed to be sacred to the darkened mind of the desperate king. David's connection with Samuel aroused the jealousy of the king, lest he who was revered as a prophet of God throughout all Israel should lend his influence to the advancement of Saul's rival. When the king learned where David was, he sent officers to bring him to Gibeah, where he intended to carry out his murderous design. PP 653.1"
"He deviseth mischief upon his bed; he setteth himself in a way that is not good; he abhorreth not evil."
Both passages describe someone plotting evil. In EGW, Saul is planning to murder David. In Psalms, the verse describes someone who 'deviseth mischief upon his bed.' The common theme is the planning and intention to do evil.
"The messengers went on their way, intent upon taking David's life; but One greater than Saul controlled them. They were met by unseen angels, as was Balaam when he was on his way to curse Israel. They began to utter prophetic sayings of what would occur in the future, and proclaimed the glory and majesty of Jehovah. Thus God overruled the wrath of man and manifested His power to restrain evil, while He walled in His servant by a guard of angels. PP 653.2"
"And God’s anger was kindled because he went: and the angel of the Lord stood in the way for an adversary against him. Now he was riding upon his ass, and his two servants were with him."
The EGW passage explicitly mentions Balaam and the angel stopping him, directly alluding to the events in Numbers 22.
"For he shall give his angels charge over thee, to keep thee in all thy ways."
The EGW passage describes angels protecting David. Psalm 91:11 speaks of God giving his angels charge over someone to protect them. The common theme is divine protection through angels.
"The tidings reached Saul as he eagerly waited to have David in his power; but instead of feeling the rebuke of God, he was still more exasperated, and sent other messengers. These also were overpowered by the Spirit of God, and united with the first in prophesying. The third embassage was sent by the king; but when they came into the company of the prophets, the divine influence fell upon them also, and they prophesied. Saul then decided that he himself would go, for his fierce enmity had become uncontrollable. He was determined to wait for no further chance to kill David; as soon as he should come within reach of him, he intended with his own hand to slay him, whatever might be the consequences. PP 653.3"
"And Saul sent messengers to take David: and when they saw the company of the prophets prophesying, and Samuel standing as appointed over them, the Spirit of God was upon the messengers of Saul, and they also prophesied."
The EGW passage directly recounts and expands upon the biblical narrative of Saul sending messengers to capture David, and the Spirit of God causing them to prophesy instead. It's more than a thematic parallel; it's a retelling with added details.