I own a company and periodically get potential employees claiming military service on their resumes (and I admittedly favor recruiting them).
No claims of medal-of-honor guys, but I’d sure like to be able to check if they got a proper discharge.
The DOD has never been particularly helpful in this regard, essentially demanding a release from the potential employee and a six-eight week waiting period.
When released from active duty, you're given your form DD-214 and told to guard it with your life. Ask to see it.