Legit reason
I've been a low-level sysadmin for the U.S. Army - what sort of bandwidth do you all think we can get from equipment we bring in on a truck? There were times when my unit was forced to block webmail and chat sites, because people were sending and receiving too many digital pictures - video was out of the question. I could literally watch my network usage peak out when the guys got open access to the NIPR, and my usage graphs always maxed out at night, when most of the official business quieted down. It is no surprise at all that the Powers That Be have made that a theatre-wide or Army-wide policy.
A lot of deployed units arrange for bandwidth through commercial providers for personal use (even Iraq has local ISPs). The troops that have access to those can still use them for MySpace, YouTube, whatever. Or they can mail home CDs or DVDs they burn on their personal laptops, and get a friend to post them - slower, but still effective. The military networks are supposed to be for government business only, we don't have the money to provide big, thick, high-bandwidth pipes - and seeing a conspiracy to censor the troops in this story requires a dedicated nutcase ready to ignore reality in favor of his pet theory. Too bad there's so many of those...