What goes first; midos or family?

When Eliezer met Rivkah and saw how greatly accommodating she was, he immediately presented her with a nose-ring and bracelets. Then he inquired as to which family she came from. When retelling the event to her father B’suel and her brother Lavan, Eliezer said that he first asked her about her family, and only then gave her the nose-ring and bracelets. Actually, that seems like the proper way for Eliezer to have proceeded, for otherwise perhaps the girl was actually totally unfit to marry Yitzchak. Rashi explains that for this very reason Eliezer changed the order when recounting the episode. If so, why indeed did he give her the presents before any investigation? (See Rashi and m’forshim) We had a thought that perhaps he wished to maintain an emphasis on the good deeds of the girl herself, and not on the family. Were he to first ask about the family it would seem as though that were the basis for the match. In truth her family was not the reason for the shidduch, it was merely the condition. Obviously however, such putting idealism before practicality would not sit well with B’suel and Lavan, and so Eliezer wisely changed the order when retelling what had happened.