I just read your explanation on equal averages and then this text.
I don't understand how you can talk about a "closed" system in this case if men in your statistics might count encounters with "sex professionals" in the number of partners they give. But on the other hand, the female "sex professionals" were not asked (as you stated in the text).
For me that means the system is not closed. As the group of possible sex partners for men is much larger (female professionals & amateurs (haha ;)). But the women asked are only the "amateurs".
At the same time, I don't have any numbers, but I think observation in this case is enough: the number of women going to male "sex professionals" is tiny.
What am I missing? I think most men would count those encounters with the professionals even if you ask them not to ;)