It's called the Berry Amendment. Any and All US Military issued equipment must by law be made in the USA unless no supplier is available and then only from trusted Allies. IE Made in China on the back of any US military kit would be a NO NO and congress would throw a Conniption.
For MRE's and training manuals the most common form of Illicit Export is incidental sale Some one gets a Real military product like MRE'es from a friend or at a PEX and then passes it on and it eventually ends up on Ebay. Or passed from one person to another via luggage or mail and it ends up in surprising places.
MRE's are Officially not really supposed to be Sold to civilians Period. They are officially Government property and there for not for resale. Yet they are the most common form of leakage of government property and really no one is going to get slapped for it unless your the supplier and they were meant for troops deployed otherwise it's just back stock that would be taking up room in a Warehouse and often by the time it leaks to the civilians it's usually pretty close to the expiration date.
basically the Army doesn't even worry about them. a good camping story can get you MRE's hell I just ordered Some on Line well posting this.
Training manuals teach the basics of doctrine and can be dangerous as they can allow enemy Intel into mindset and operations. but it's also low pole stuff
Uniforms and Vests Also tend to be second runs and commercial stock.
Other things are more worry some like Actual issue night vision and Electronics as those are more sensitive. MRE's okay, Manuals I could get at the base PEX fine. knock off uniforms ah... not good but not end of the world. Actual serial numbered US GOVERNMENT PROPERTY. NO go, The chips and sensitive parts again No go.