Apparently nobody here remembers American Pie 2 and the "Rule of Three." In that movie, the Rule of Three was a simple rule that said that for men, divide the number of women he says he's slept with by three to get the real answer; for women, multiply it by three to get the real answer. It seems apparent to me that that's what's causing the discrepancy in these studies: men may overstate their number of sexual partners, while women may understate theirs.
What's more, I think differences in the way men and women are socialized regarding sex play a big role. Men are socialized to view sexual promiscuity as an accomplishment, looking up to other men who "hook up" with a lot of girls, etc. Men also tend to be less selective than women when it comes to sex. I'd actually argue that many of the men in this survey -- save for perhaps a few of those who said they'd had 15 or more partners -- are being honest. Because sex is such a big deal to men, and because sexual promiscuity is viewed positively, many men view each sexual encounter as a "conquest," and they'd be pretty likely to remember it.
For women, on the other hand, sexual promiscuity is viewed negatively. They may be willing to fudge a bit on the number, so that (even in an anonymous survey) they're not viewed as a slut. Women also have a tendency to think that some sex partners "don't count." As Chris Rock said, when you ask a woman how many men she's slept with, she'll tell you how many boyfriends she's had. For all we know, women are counting the number of long-term boyfriends they've had and ignoring their short-term sex partners or one-night stands, and men would probably count such things.
Finally, there's a difference between the median and the mean. One woman who's slept with 100 different men would alter the mean quite a bit, but it wouldn't change the median that much, if at all.