If you don't do the overt conversion, you are at the whims of the software and your settings to make sure that the cell sizes, snap raster, etc etc are all good. Sadly, the Environments tab on the tool doesn't flash so that the user checks those prior to doing a run. The required information is definitely in the long detailed help topic.
As an alternative, I don't suppose you have an advanced license?
Tabulate Intersection—Help | ArcGIS Desktop