The hormone claim means that there could be a causal link. However, these hormones (oxytocin and prolactin) are released during breastfeeding and other normal activities. These hormones are therefore released during the course of other activities, and isolating their potential effects to just orgasm is tricky.
One population to examine are nulliparous (never had a child) women and men, as these groups won't be lactating; however, oxytocin is also associated with social behaviors and is known as the 'love hormone', so again, isolating orgasm as a sole producer of sufficient oxytocin to reduce breast cancer risk is difficult. It may also be that all the social activity leading up to and after orgasm also causes oxytocin release, in which case orgasm may not be the sole cause of any risk reduction.
Prolactin is also a hormone that does more than just orgasm response:
more than 300 separate actions of PRL have been reported in various vertebrates, including effects on water and salt balance, growth and development, endocrinology and metabolism, brain and behavior, reproduction, and immune regulation and protection
There is a slight reduction in risk associated with breast feeding (again, relevant because these are the same hormones):
After adjustment for parity, age at first delivery, and other risk factors for breast cancer, lactation was associated with a slight reduction in the risk of breast cancer among premenopausal women, as compared with the risk among women who were parous but had never lactated (relative risk, 0.78; 95 percent confidence interval, 0.66 to 0.91); the relative risk of breast cancer among postmenopausal women who had lactated, as compared with those who had not, was 1.04 (95 percent confidence interval, 0.95 to 1.14). With an increasing cumulative duration of lactation, there was a decreasing risk of breast cancer among premenopausal women (P for trend <0.001) but not among postmenopausal, parous women (P for trend = 0.51). A younger age at first lactation was significantly associated with a reduction in the risk of premenopausal breast cancer (P for trend = 0.003). As compared with parous women who did not lactate, the relative risk of breast cancer among women who first lactated at less than 20 years of age and breast-fed their infants for a total of six months was 0.54 (95 percent confidence interval, 0.36 to 0.82).
These are some of the same hormones released during orgasm; as such, these hormones might cause a risk reduction. A causal link was hypothesized in 1995:
Sexual activity in nulliparous women also protects and OT levels have been shown to rise with orgasm in women and in men. OT systems in the brain are intricately linked to oestrogen and progesterone levels, and it is possible that these hormones may modify the OT secretory response both centrally and through an effect on the sensitivity of the breast.
However, most searches for breast cancer and orgasm relates to the sexual activity of survivors, rather than the possible preventative technique of frequent orgasm.
tl;dr: There may be a link, even a causal link, but the effect appears to be pretty slight, and difficult to isolate relative to the other producers of the hormone.
