Ah, I see. I misunderstood. When I read
I click OK and the geometry (the Drawing) imports but no fields
I read that as though you did have some fields in the drawing but they did not import.
If you don't have any fields in the drawing (other than the geom or mfd_id) then you end up with a DBF that has no attribute fields, and that's not a shapefile as the ESRI standard is written, with the resulting import message as Tim has noted.
8 is applying the shapefile standard as it is written. If a DBF doesn't have any fields to it, it's not a shapefile. If you tell 8 it is a shapefile, but when 8 looks and sees that it is not a shapefile, it advises you that it is corrupted, but then goes ahead and does its best to import it anyway, importing it fine with no fields. You can even delete the DBF entirely and 8 will still import the shapefile.
This is one of those cases where whichever way you second-guess erroneous use of a standard, you're going to get it wrong for some people. For example, 9 could advise people that a drawing with no attributes can't be exported to shapefile format as a legal shapefile. That would drive people nuts, so instead 9 exports it as a "shapefile" that isn't strictly standard but which everybody can use.
Another way for 9 to do this would be to automatically add a field if there aren't any, like an ID field. That, too, would be annoying to some people who don't want their software adding a field, just to make software happy that applies standards as they are written. Maybe that could be an option, turned on by default.