Thank you gerickecook!!!
This was driving me nuts. I tried every possible snap to raster setting and finally came to the forums. I didn't find your post until I googled "site:forums.arcgis.com snap raster not working" and limited my results to the past year <sigh>.
turning off background geoprocessing worked for me, and I was able to do the processing from within ArcMap and get a snap. Unfortunately (for me) turning off background geoprocessing looks like it breaks the "overwrite geoprocessing outputs" option. When I try to run the tool and overwrite a dataset, I get two errors: (1) The table already exists, and (2) No spatial reference exists. Renaming the output worked fine (I was working with file geodatabase rasters).
Seems like this would be a big deal. hope it's fixed soon.