Sam2: I believe you are misquoting Rabbi Broyde. He does not hold it is lechatchila muttar for a woman to not cover her hair. He wrote that article to be melamed zchus on the women who don’t, by providing possible halachic basis, but he does not pasken that way.
See Michael J. Broyde, Hair Covering & Jewish Law: Biblical and Objective (Dat Moshe) or Rabbinic and Subjective (Dat Yehudit)? available at http://www.traditiononline.org/news/_pdfs/0095-0180.pdf