There are many proofs that this is indeed so. (Among other things, meforshim who say differently.)
One interesting one is in Rabbenu Bachya on this week's parsha. The pasuk Bereishit 24:19 states:
|יט וַתְּכַל, לְהַשְׁקֹתוֹ; וַתֹּאמֶר, גַּם לִגְמַלֶּיךָ אֶשְׁאָב, עַד אִם-כִּלּוּ, לִשְׁתֹּת.||19 And when she had done giving him drink, she said: 'I will draw for thy camels also, until they have done drinking.'|
הגבורה הזאת לשאוב לכל גמליו לא היה בחוק האפשרות כי אם בסיוע אלהי וכל שכן לפי דעת המדרש שהיתה בת שלש שנים אבל היה הענין מכלל ההצלחה שהבטיחו אברהם: הוא ישלח מלאכו אתך והצליח דרכך
This strength the draw water for all his camels is not within the natural possibility, except with Divine assistance. And certainly according to the opinion of the midrash that she was three years old. However, the matter was within the general "prospering" which Avraham promised him. Bereishit 24:40:(Brief digression -- this "pasuk" Rabbenu Bachya is citing here is actually a conflation of two pesukim: This pasuk #40, and pasuk#7:
We see two points from Rabbenu Bachya. First, he is willing to say that a maiden drawing water for all the camels is impossible, and certainly that a three year old girl drawing all that water is impossible. The difference is that he is willing to read this into the text as Hashem's special providence and assistance, such that he is willing to stand by the midrashic reading.
Second, he appears willing to argue with the midrashic reading. He states וכל שכן לפי דעת המדרש שהיתה בת שלש שנים, implying that this is the opinion of the midrash, but that one could assess the text differently and that this would be a legitimate reading. But that there would still be Divine assistance at play here, since it would still be impossible.
This grants legitimacy, if any is needed, to readings of the story such that Rivkah could not possibly be three years old, or else she would not be able to draw the water (, converse with Eliezer, agree to marry, etc.)
On a related note, see my post from last year about the plausibility of a three year old Rivkah.