I don't have a copy of the UCMJ handy and with that thing being as enormous as it is I doubt I would want to sift through it anyway but I did find some stuff out of the PFE which takes pieces from the UCMJ so here goes:
"All DoD employees are prohibited from recieving pay or allowance or supplements of pay or benefits from any source other than the United States."
"DoD employees may not receive additional pay or allowance for disbursement or public money or for the performance of any other service or duty unless specifically authorized by law."
and under related prohibitions:
"Receving honoraria for performing officials duties or for speaking, teaching, or writing that relates to one's official duties"
I guess this stuff could be interpreted in several ways depending on how you look at it. I interpret by "United States" they mean the government. We're in an exercise right now and I'm working nights but when I get a chance I'll call the base legal office and ask them. I should be able to get a straight answer and a UCMJ reference for ya one way or the other.
In fact I will even call them and ask "Hey if I capture Saddam can I accept the 1 million dollars that Bruce Willis is offering?" they oughta get a kick out of that.