Intent, I suppose, but then again I'm not a lawyer!
Let's say, in this hypothetical scenario, we take two douchebags at a bar. One tells a chick that he's a renowned cardiac surgeon and gets laid, then continues to feed her this line for weeks and she buys all of it. The other tells her he's a Navy pilot and gets laid (stay with me here, it's a fictional story), then also keeps up this charade successfully for some time.
Which is the bigger asshole? I agree, as would most people here, that the one impersonating the vet is worse, because of all the people who've sacrificed their lives wearing the uniform, etc. A doctor might have a different opinion--the other guy is pissing on a noble profession, too, the Hippocratic Oath, etc.
Regardless, they're both basically doing the same thing, with the same intent--lying about who they are in order to gain respect, admiration, and in this case, pussy.
As far as the Constitutional law aspect, I'm not going to claim any special expertise, other than being a follower of such things. However, one of the great things about the Constitution is that it protects us all by preventing the good idea fairy from pissing all over our rights. People get riled up over the problem of the moment, and often try to enact measures that, in the long run, are really bad ideas. Suspending Habeus Corpus, the Alien and Sedition Acts, banning flag burning, things like that. It slows our roll, and makes us put some thought and rigor into things. That's why amending it is so damn hard.
Now, unfortunately, we've steamrolled over several rights in the interests of GWOT, to use another current example. The war on terror is a great cause, as is preventing asswipes from impersonating veterans, but neither is worth weakening any rights to do it.
Can you demonstrate a harm that falls outside of fraud (I.E. that's not resulting in personal gain or harm to another) that would merit additional statutory relief?
