You are right,it is hard to do definitive research.But why do women take a chance in the meantime given the suggestive evidence:the Singer work,breast pain caused by bras, etc. Doctors say it's a myth that bras cause breast cancer while at the same time saying they don't know what causes it. And how could they possibly know without research anyway? More likely they don't want to be responsible for ruining the bra industry.
Do women feel they have to look "busty" to get attention and being braless is flat and saggy? Believe me, if they don't try to conceal being braless there will be plenty of attention.