I believe the policy is flawed. If a man has the option to expose his chest (privately) for screening, then a woman should have the same option. Denying that option to women is based on an erroneous belief that women's breasts are sexual organs. They aren't.
It almost reminds me of the old issue about men being able to walk around in public without shirts on, whereas women are not allowed to do so (during hot summer months, on non-topless beaches, etc.). It seems to reinforce and idea that women need to possibly be "ashamed" of their bodies by always needing to be covered up.
In terms of the specific issue of the airport screenings and privacy... I think both sexes should have both options. If men want to have privacy, they should be allowed that (just as women are). And, if women want the convenience of just removing the thing in the more public areas, then that should be allowed too. It does seem odd that it's automatically assumed that women need to be secluded off to do this.
Although, personally I can understand wanting privacy.
And, LOL, yeah, nipple rings on women can be fairly substantial.