"The king did not compel the Hebrew youth to renounce their faith in favor of idolatry, but he hoped to bring this about gradually. By giving them names significant of idolatry, by bringing them daily into close association with idolatrous customs, and under the influence of the seductive rites of heathen worship, he hoped to induce them to renounce the religion of their nation and to unite with the worship of the Babylonians. PK 481.1"
"Lest thou make a covenant with the inhabitants of the land, and they go a whoring after their gods, and do sacrifice unto their gods, and one call thee, and thou eat of his sacrifice;"
Both passages deal with the subtle influence of pagan culture and the danger of compromise. The EGW passage elaborates on the methods used to assimilate the Hebrew youth, while Exodus warns against making covenants that lead to idolatry.
"At the very outset of their career there came to them a decisive test of character. It was provided that they should eat of the food and drink of the wine that came from the king's table. In this the king thought to give them an expression of his favor and of his solicitude for their welfare. But a portion having been offered to idols, the food from the king's table was consecrated to idolatry; and one partaking of it would be regarded as offering homage to the gods of Babylon. In such homage, loyalty to Jehovah forbade Daniel and his companions to join. Even a mere pretense of eating the food or drinking the wine would be a denial of their faith. To do this would be to array themselves with heathenism and to dishonor the principles of the law of God. PK 481.2"
"But Daniel purposed in his heart that he would not defile himself with the portion of the king’s meat, nor with the wine which he drank: therefore he requested of the prince of the eunuchs that he might not defile himself."
The EGW passage directly refers to Daniel's decision not to defile himself with the king's meat and expands on the reasons behind his choice, connecting it to idolatry.