I have to agree with you, handfleisch, that militarism is a dirty business in many ways. When a military organization sets up shop, they of course know that prostitution will greatly increase in the area regardless of how they respond to the problem. If they do nothing, they will put their soldiers at risk for disease, theft, and other issues. Whether they encourage certain local organizations to improve hygiene standards or become active participants in the trade, they will have dirty hands and plenty of opportunity for corruption within their own organization.
While the military will doubtless take whatever action they feel warranted to protect the troops, they may or may not consider the welfare of the women in the trade, depending on their moral values. They have already stepped so far over the line of behavior generally considered ethical that it is questionable if the affected women's interests will get much of a hearing.
Again, you seem to be highlighting the military, whereas it is really a problem that is universal. You could easily take the military out. If an expat should be party to a rape in a foreign country, regardless of being of the military, he'd hesitate too with reporting it, particularly if it is against the law of that country.
There is a mixture of blame here. Availability of prostitutes, failure of the Government of the host country to check on the situation, and of course also failure of the visitors' country of origin - whether Government agencies or companies - to monitor it closely too. If there were no prostitutes around, or if prostitution is made into a VERY heavy penalty crime (like with drugs for example making it into a capital offense), I can't see how they would get involved in it. But it would probably be unrealistic for the host country to really do anything about it as it is of course scoring in other ways by having the military/other companies around. Unless its locals would complain heavily about prostitution, it may just look the other way.