The clerk at your local store is simply uninformed. Any router can be mounted in some kind of table - even Dremel tools. The router bits don't get dizzy by being upside down. In many cases, however, it is the larger routers (2 to 3+ HP) that are used in tables to enable the use of larger bits for profiling and joinery cuts. Those larger routers might be uncomfortable for many to use hand-held because of their weight.
The added utility of table-mounted routing is that one has a large fixed surface (the table) and a large, stable guide surface (the fence) against which the work piece can be guided (usually with push blocks and such, to keep fingers well away from the bits). The combination allows work on stock that has a relatively small cross-section, and in a safe manner. In contrast, hand-held routing is usually done on larger pieces where the work piece itself is the stable surface.
Both techniques are useful, and safe, if done properly.