Shulchan Aruch Yoreh De'ah 242:32:
הרב המובהק שמחל על כבודו בכל הדברים האלו או באחד מהם לכל תלמידיו או לאחד מהם כבודו מחול ואף על פי שמחל מצוה על התלמיד להדרו (ואסור לבזותו)
A rav muvhak [someone from whom one gained a majority of his Torah] who forgoes his honour in all these matters [including standing for him (see 242:16)] or in one of them, to all of his students or to to one them, his honour is foregone. Even though he forgoes his honour, it is still a mitzvah for the student to grant him some form of respect (and it is forbidden to disgrace him).
So it would seem, according to the dichotomy which you presented, we are standing for the man himself and not for the Torah.
However, if we look at the source for this ruling in Kiddushin 32 we see that it is a little more subtle:
רב יוסף אמר אפי' הרב שמחל על כבודו כבודו מחול שנאמר (שמות יג, כא) ויי' הולך לפניהם יומם אמר רבא הכי השתא התם הקדוש ב"ה עלמא דיליה הוא ותורה דיליה היא מחיל ליה ליקריה הכא תורה דיליה היא הדר אמר רבא אין תורה דיליה היא דכתיב (תהלים א, ב) ובתורתו יהגה יומם ולילה
And Rav Yosef says: Even with regard to a rabbi who forgoes his honor, his honor is forgone, as it is stated: “And the Lord went before them by day” (Exodus 13:21). God Himself, the Teacher of the Jewish people, had forgone the honor due Him and took the trouble to guide the people. Rava said: How can these cases be compared? There, with regard to the Holy One, Blessed be He, the world is His and the Torah is His, and therefore He can forgo His honor. By contrast, here, is it his Torah, that the teacher can forgo its honor? Rava then said: Yes, if he studies, it is his Torah, as it is written: “For his delight is the Torah of the Lord, and in his Torah he meditates day and night” (Psalms 1:2). This indicates that at first it is “the Torah of the Lord,” but after he studies, it becomes “his Torah.”
Rava appears to be teaching us that we are indeed standing up for honour of the Torah, but inasmuch as the Torah "belongs" to the Rav, it is within his gift to forego the honour due.