The study that suggests that has been brought up in several circles whenever PCOS and TDEE are mentioned. I've read through what I have access to and am personally rather skeptical about it. As I recall, the only thing it did was measure the metabolic rate of various women with PCOS with and without Insulin Resistance. While they did find that women with PCOS and Insulin Resistance have a lower metabolic rate, there's not enough information to determine whether it's the PCOS itself that causes it, since it's very common for such women to eat very low calorie diets (to the tune of no more than about 800 calories a day, plus an hour+ of exercise), which is also known to lower metabolic rate.

As a women with PCOS and IR, though, I've found that if I take the time to find out what foods are doing me harm and eat only the foods that don't do me harm, I can eat a sane amount of food (roughly 2000 calories worth, at 5'9") and lose weight. This has resulted in a diet that greatly restricts what I eat normally, but I find it far more freeing and successful than trying to only restrict how much I eat (which failed miserably for me for close to a decade).

The thing with metabolic rate is that it changes in response to outside stimuli, including not only how much food we eat, but also what kinds of food we eat. Different foods affect our hormones and metabolism differently, and while any given thing might only alter it by 50-100 calories, when you have a dozen of such things, suddenly you've altered your energy expenditure by an amount that can affect whether you lose or gain weight.

We absolutely do not. Studies done show it ranges on average from 300-500 calories lower than the average woman.