Did he lower his neck and stretch out his nose a bit while he did it? If so, it's a "baby face" submissive motion. Not sure why he would offer it on the lunge line, but that's what it sounds like he was doing.
Keep us informed about how it progresses, it's interesting.
EDIT: Maybe you could take a video for us to see?? Might help, besides, we like pictures and videos!
Edit again: Just saw the picture of the arab, he's chewing on the bit of his show halter. You say yours had no bit though...hmmm. Even more interesting.