As others have noted, the term "stolen valor" isn't really applicable to modern people portraying historic events--if someone at a reenactment is wearing a medal and claiming it was awarded for his heroic actions at the Battle of Gettysburg, he'd just be considered a nut case.
I get what you're saying though, but reenactments are just that--reenactments. An attempt to portray as best we can a semblance of what a Civil War conflict might have looked like, minus the blood, guts, and flying body parts, of course. And no matter how authentic our kit, we still go out there in good health with full bellies and without dysentery, body lice, filthy clothing we've worn for months, intestinal parasites, etc. A reenactor would be delusional to believe that anything he does is "still living that experience."