Let's look in context:
11 In the Lord, however, woman is not independent of man, nor is man independent of woman. 12 For as woman came from man, so also man is born of woman. But everything comes from God. 13 Judge for yourselves: Is it proper for a woman to pray to God with her head uncovered? 14 Does not the very nature of things teach you that if a man has long hair, it is a disgrace to him, 15 but that if a woman has long hair, it is her glory? For long hair is given to her as a covering. 16 If anyone wants to be contentious about this, we have no other practicenor do the churches of God.
I didn't intend to start a doctrinal debate, but to attempt to answer the question posed in the article. The question of women wearing veils doesn't have anything to do with sexual misconduct of priests. I believe the celibacy issue does.