Your somewhat crude remark is right on the money - so I'll repeat it: Yes, we just need to get them laid.
I have believed for some time that the primary thing that differentiates Islam from other religions is the level of control that the religious leaders exert on the sexual behavior of their followers. Now this is not unique to Islam as any churchgoer can tell you but the extreme measures that are imposed on those of the Islamic faith are, to say the least, extreme.
This control of sexual behavior represents, IMHO, a denial of the very essence of human nature which can be summed up as (in most but not all cases): Boys like Girls and Girls like Boys. This denial dominates the everyday life of those who live in the Islamic world, basically as a result of the extreme limitations that are placed on the behavior and dress of women. They are basically denied their fundamental right to attract a mate, the very thing that, as we all know, they do so well.
So the bottom line is that I agree with author of the article. You have a bunch of frustrated young men with no access to female companionship and you promise them 72 virgins for ones days work (and incidentally, their life) and you get lots of volunteers. Get them laid and the problem does go away.
I would think that knowing that you might not be able to have children of your own would have a lot to do with frustration. Sex is important because the urge for reproduction is important.