One can like very much that it says this in the Shulchan Aruch. But it has nothing to do with women driving.
That is true. And, indeed, those that posit as such permit women to drive. Those that posit the aforementioned Shulchan Aruch is relevant to women driving, posit that it is impermissible for them to drive. Both halachic positions exists among various poskim.
Rav Vozner paskens that women should not drive:
http://www.hebrewbooks.org/pdfpager.aspx?req=1414&st=&pgnum=9&hilite=