Avi – that may have been the case back then, but it is not the case today. The girls in every Bais Yaakov know the basic halachos of tznius. And all seminaries (BY or otherwise) teach hilchos tznius.
In one (modern/modern orthodox) seminary I taught in, the issue of tznius was being discussed at a teachers’ meeting. One of the teachers said when she administered a test on hilchos tznius, there were girls who were sitting there wearing short sleeves as they were taking the test and writing the sources about how your upper arms have to be covered!