The stream layer is a polyline layer. The "walls" are known watershed boundaries and this is the form of a polygon layer. I recall trying to use a polyline layer for the walls at one time and having it work, but I usually use a polygon layer.
What Arc Hydro does is, it takes the DEM that streams are being burned into and it reduces the elevations of the cells that intersect the streams polyline plus the buffer(s) by the amounts you set. Then the elevations of the cells the wall polygon perimeter intersects (or the wall polyline intersect) are increased by a amounts you set (use at least 2 grid cells).
The final DEM, in fact, can have very deep streams and very high walls. The goals is not to create a perfect DEM from which accurate contours can be made. What you want is an accurate flow direction grid. That then becomes the basis for your flow accumulation grid, etc. I do the fill after burning stream and building walls just to make sure the bottoms of the fill streams don't have any localized low points that will mess up the flow direction grid.