Yes the facts generally are there. Keep in mind, inclusive of support functions, there are many aspects of military operations that we may not necessarily consider HARD military, but they are key to successful operational function and accomplishment that are contracted out and done so successfully. Vinnell Corp is an example; they do a lot of overseas work for the US in the Gulf region and Middle East, such as Turkey. We have Bombardier and ATCO Frontec.
www.vinnell.com
Companies such as MPRI have provided direct military contract services for the US in the Balkans training certain military forces there.
http://www.mpri.com/channels/home.html
Another company that provides discrete support to the US abroad is Dyncorp, read between the lines if you have to.
http://www.dyncorp.com/areas/index.htm
For your reading pleasure you can explore the following link:
http://free.freespeech.org/napalm74/main.html
An area that many overlook is air operations. This is considered a prime military function; the CF has on numerous occasions used heavy lift from other militaries and private firms. The United Nations does this as well, especially within Mission Areas. Private contract air operations are the buzz of the day. Rarely do you see military airlift in support of missions, unless the tasked nation provides their own, usually in support of their contingent.
There are numerous reports or purporting of private firms out there providing military contract services to the UN and in support of various national government foreign ventures.
Some are true many are not. But this move is based upon economic reasons, not some underlying motive. Standing military forces are not cheap and if you only need this service once in a blue moon, why not contract someone. Especially if that lucrative diamond interest, oh sorry, I digress.
There is a lot of good info out there, and if you wish to dig deeper, have fun.