Only half true, not every western society was made entirely of arranged marriages; those were the norm in aristocratic circles, but for people closer to the bottom of the pyramid it wouldn't matter as much.

Women always had less rights in general in the west, especially after Christianity took over, but it wasn't a case of "every woman has always been at a real peril of being killed if they're seen openly flirting with a man" - similar to how not every Christian country has made prostitution illegal, not even back in colonial times, or how even when it was, it wasn't equally enforced everywhere.