Why does Rashi mention that the geder is made of stone?

Summary: An interesting Taz on Rashi, but I find my own way.
Post: In parashat Balak, the malach stands in Bilaam's way in a narrow path between two vineyards:

24. The angel of the Lord stood in a path of the vineyards, with a fence on this side and a fence on that side.

כד. וַיַּעֲמֹד מַלְאַךְ יְ־הֹוָ־ה בְּמִשְׁעוֹל הַכְּרָמִים גָּדֵר מִזֶּה וְגָדֵר מִזֶּה:

Rashi explains:

with a fence on either side: Heb. גָּדֵר. Unless specified otherwise, גָּדֵר refers to one made of stone.

גדר מזה וגדר מזה: סתם גדר של אבנים הוא:

What is his basis for saying this? Why should it matter? What does this add?

The Taz wonders about this Rashi.

First, in terms of the dibbur hamatchil. Why not just cite גדר, as opposed to the full phrase. Secondly, why does it matter if the fence was made of wood or rock?

He answers based on a midrash Rabba -- also a Tanchuma, that refers to the merit of the Israelites in having the luchot of stone, which were written upon on both sides. Thus:

גדר מזה וגדר מזה. אין אתה יכול לשלוט בהם, שבידיהם שני לוחות אבנים כתובים מזה ומזה משני עבריהם. 

And despite the midrash not mentioning stone explicitly, by Rashi mentioning stone, and by Rashi using this phrase which is darshened in this way in midrash, he is hinting to this. And the chacham harazim can see wondrous things, on condition of course that the specific language of the dibbur hamatchil really indicates this.

An interesting approach. But if Rashi wanted to indicate this, he could have told us more explicitly, by citing the midrash. I would rather look to see how this comment of Rashi fits in with other comments of Rashi, and try to develop some sort of picture of Rashi's agenda from that.

Mekorei Rashi refers us to Bava Kamma 29b, where Rashi makes the same statement, in explaining the gemara. Thus:
והגודר גדרו בקוצים - שעשה גדר של קוצים דסתם גדר של אבנים הוא דכתיב וגדר אבניו נהרסה (משלי כד):ש

Thus the Mishna needed to indicate the material for the geder because it was not the implicit one. A typical geder is a stone wall. His proof from this is Mishlei 24:

לא  וְהִנֵּה עָלָה כֻלּוֹ, קִמְּשֹׂנִים--כָּסּוּ פָנָיו חֲרֻלִּים;    וְגֶדֶר אֲבָנָיו נֶהֱרָסָה.

31 And, lo, it was all grown over with thistles, the face thereof was covered with nettles, and the stone wall thereof was broken down.

Perhaps since the pasuk did not indicate otherwise, Rashi thought it a good point of peshat to give a precise definition of term. However, I think it is more than that. Namely, in the next pasuk and Rashi:

25. The she-donkey saw the angel of the Lord, and she was pressed against the wall. She pressed Balaam's leg against the wall, and he beat her again.		כה. וַתֵּרֶא הָאָתוֹן אֶת מַלְאַךְ יְ־הֹוָ־ה וַתִּלָּחֵץ אֶל הַקִּיר וַתִּלְחַץ אֶת רֶגֶל בִּלְעָם אֶל הַקִּיר וַיֹּסֶף לְהַכֹּתָהּ:
She was pressed: וַתִּלָּחֵץ. [The ‘ niphal’ form denotes] she herself.		ותלחץ: היא עצמה:
She pressed: וַתִּלְחַץ. [The ‘kal’ form denotes that she pressed] something else, namely, Balaam’s leg.		ותלחץ: את אחרים את רגל בלעם:

If pressed against wood or thorns, it might injure but not crush. But with a stone wall, it is a more serious injury.

Indeed, in Sotah 10a, we read:

R. Johanan also said: Balaam was lame in one leg, as it is said: And he went shefi;

While in next perek, where this pasuk occurs, Rashi does not explain it that way, I would guess that this was in the back of his mind, that Bilaam here becomes lame of a crushed foot. A punishment for the wicked.

As to why cite the full phrase rather than just geder, if it is indeed significant, it can indicate how he was between a rock and a hard place, and how the situation was such that whichever way the jenny turned, she would cause an injury to Bilaam. And we can thus anticipate this injury one pasuk early. And this foreshadowing is part of the meaning of the pasuk.