I got a silver laurel twice already...I am thinking maybe she gives stat items?

Yes she does give three different kinds of laurels. I'm pretty sure if you visit the battle form they have a stat booster list and where to get the items and most of them come from her.

She's been giving out the laurels since I joined 2 years ago. XD

Those are Shinwa-exclusive, they just don't have "Shinwa" in the name.