I just found this:
http://www.mreinfo.com/mres/us-govt-vs-ebay-auctions/
No actual statute (US Code) is cited, and, DLA is using different tactics to get them off eBay, leading one to believe the "illegality" is more hype than reality.
The US Postal Service claims "misuse" of their free Priority Mail boxes is illegal, too, but I've asked for a statute, and none is forthcoming.
So, it's a gray area. I wouldn't want to be a test subject in Federal "court," but I imagine quiet sales are no real problem. Getting caught as a soldier/sailor selling them is quite another problem, indeed.
The military personnel prohibition apparently stems from the great personal profits made during Katrina of pallets of MREs "liberated" from military stocks and sold privately.