Interesting. I've had the processing extents off before which will clip the results vertically and/or horizontally due to a reduced processing extent. I don't think I've ever had it "mask" the results to the AGREE Streams.
Are the elevations in the resulting AGREE DEM valid? All I can think of is maybe the Raw DEM layer that the tool is defaulting to is not the "rawdem" raster. When I use Arc Hydro I always use the default raster, dataset names. This saves some time and reduces some errors.
A while ago I couldn't get the DEM Reconditioning to work. I now don't recall if it crashed or did what you are experiencing. In the end I developed my own Model Builder model to do that work. Took a bit to get the logic right and creates a bunch of intermediate rasters (likely the tool does too). It has worked well enough for me that I don't use that part of Arc Hydro. A screen shot of is is below.
At some point I'll try the DEM Reconditioning tool again. I'm learning Python bit by bit and may eventually turn to that. Python appears to have less problems than Model Builder. Also, I hear that ArcGIS Pro Model Builder will be more stable due to the 64 bit compatibility.
Mark