It won't be $15 -- but an affordable player that is great with Rockbox is the SanDisk Clip+. It's got a decent screen, really small form factor, microSD.
My main Rockbox'd unit is an iPod Video (5.5) with an iFlash Quad (up to 4x microSD cards) and a 2000mAh battery. Not the most expensive project, but not as cheap as the Clip+.
My guess is that the parent is talking about the Sansa c200 or something similar.