Well, clearly there's a big difference since we're not claiming to actually exist in the medieval period.
All that aside, honest portrayal certainly has educational value, but there's no honor at all in claiming achievements that never were.
For instance, if he were at a reenactment event and portrayed a SEAL, it would be no big deal. But he dishonors himself, and the SEALs, by claiming to have been one in the real world when he didn't complete the training.
I was reading a while back about the concept of "stolen honor". Apparently it's pretty widespread. Since you can go online and order uniforms and medals, people will buy these things and pretend to have earned them the hard way. I even ran across a website (can't remember the URL) that was dedicated to exposing public acts of stolen honor. One example was embarrassingly over the top. The guy put on just about every high-level medal our country bestows.
But going back to knights... I think as long as we're honest about what we're doing, we're fine. We're not knights via an official knighting in a country that still does that, and we're not medieval knights since we live in the modern age. But we're knights of our organization, and we're portraying historical knights. And if we're taking chivalry seriously, then we're re-awakening the aspect of knighthood that is our cultural heritage, and we can call ourselves knights. We have the added advantage here that since it's a historical re-creation, it's obvious that we didn't spend years as a squire in medieval Europe, so no one is going to be accidentally mislead.
And of course, as I noted above, being knights of our own organization is an important aspect. In a way it adds legitimacy, since any private organization is free to use whatever ranks or titles it wants internally. So if that title is "knight", then no one can dispute that.
We just have to watch out for the rare few people that will think we're being delusional. Not that it would ever happen (*cough*facebook*cough*).