Lilmod,
Joseph – not true. btw, I have heard that according to Halacha, since common courtesy nowadays is that the guy let the girl go first, he is SUPPOSED to let her go in front of him even though according to tznius it should be the other way. Apparently, we do believe in chivalry.
You haven’t quoted where to find it and anyways I see that you said anywhere within sight is a problem, usually when someone says ladies first she’s in sight