Simple test to that question:
Can a private citizen walk onto a secure military installation?
If not, does it follow that the authority of the Federal Government extends to civilians when it comes to military property?
(Do you see where this is going?)
If the ribbons are protected intellectual property under the Lanham Act of the U.S. Military (and they are), then the extension of the protection of that property from unauthorized use does extend to civilians.
In other words, wearing a ribbon that has been trademarked by the U.S. Military extends the control of the U.S. Congress to the wearer. Just as stepping onto a secure military installation puts you under the rules that govern that property.
And just as there are stiffer penalties for trespassing onto a secure military installation than, say, trespassing on your neighbors property, the U.S. Congress can establish stiffer penalties on wearing certain trademarked items without authority than might otherwise be established in local or State laws.
At least that is how I would argue the case from the Federal Government's point of view.
ASB: “Can a private citizen walk onto a secure military installation?”
Not if they claim to be a member of the military when they are not, but that’s not the same thing as bragging in a bar.
ASB: “In other words, wearing a ribbon that has been trademarked by the U.S. Military extends the control of the U.S. Congress to the wearer.”
No more so than wearing a jacket with “Mt. Dew” on it puts you under Pepsi Co corporate rules. It depends on how a trademark is used. If you use it for personal gain, such as selling jackets marked “Mt. Dew” that you made on your own, then you have a point. Otherwise, no.
In my opinion, the only person potentially harmed would be the redhead who goes home with the fake war hero. Perhaps she could sue for damages?