Rashi did indeed have a different Mesorah, as well as many other Jews. The differences weren't as significant as those between our Mesorah and, say, the hypothesized Hebrew vorlage of the Christian LXX, but they were there. One aspect of these differences are the "אותיות משונות" (strangely-shaped letters), discussed more broadly by Moshe Rosenwasser in his paper "האותיות המשונות בתורה", Ha'Maayan 46, pp. 22-40 (link to the entire volume).
According to him, some centuries ago scribes stopped copying strangely-shaped letters and made them into regular letters. In his opinion, Rashi's backward Nun in Charan is one example of such a strangely-shaped letter.
Minchat Shai on the verse noted that the Or Torah did indeed find a Torah scroll which had a kind of decoration at the top of the Nun which made it look inverted. However, he (Minchat Shai) found evidence for the difference in the Mesorah in the Masoretic book Sefer Tagi (ספר תאגי), i.e. that according to Sefer Tagi there really should be a backward Nun in Charan.1
1 Sefer Tagi's exact words are "דאקים (or דעקים according to Minchat Shai's version) רישיהון ולא מזייני" - the דאקים version means that its head stands up and is undecorated (with ketarim/serifs) while the דעקים version means that its head is bent and is undecorated.