What did Lavan and Besuel mean when they said, "Take her and go... as Hashem spoke"?
Seforno: They meant that Eliezer could actually take Rivkah and leave, even without their permission, as Hashem had decreed before Yitzchak was born! 1
Ha'amek Davar: Even though Hashem did not specifically say so, what the Hashgachah shows is as if Hashem actually said it.
Refer to 24:14:2:3*.
Why did they need a special reason to agree? Even without the proof, it was good for Rivkah!
Ha'amek Davar #1: It is difficult to go to another country (Kesuvos 110b).
Ha'amek Davar #2: To marry a paternal relative is not a sign that this is the destined match, so they needed another proof.