The goal of the DEM reconditioning using Spatial Analyst or Arc Hydro tools is to get the flow direction right. When I work on the stream burning step, I try to minimize the width of the burn by making the stream buffer only 2 cells wide. You may be able to make it just one cell wide, but I vaguely recall that not working well so I've stayed with 2. I work with a 10x10 dem. The walls have to be at least 2 cells wide or you will get "leakage" via the diagonal.
I also minimize where I put the streams to burn. If the rawdem is good for the flow direction, I don't put a line in it. I only put in lines at bridges and culverts. If I have a stream layer, I will buffer the road layer and use that to clip the stream layer so I only have short segments at the stream crossings. Of course I have to review the crossings to make sure the stream polyline is "correct".
So, does burning streams introduce error. Yes. Does the rawdem have errors already? Yes. If you are diligent enough you can make the rawdem better for flow direction determination and minimize the introduced error.