Caulk or Grout the base of a toilet?
Code requires toilets to be caulked at the floor, that, IMO is a mistake. If the toilet does develop a leak, it will be restricted under the toilet and the subfloor, and may leak for a while before it is detected. So much for that.

The toilet can be shimmed to keep it from rocking. Because of the rocking, what is not leaking now eventually will leak. 
The grout that the other installer used will act as shims to keep it from rocking as well, but back at the "if it leaks" issue. If you feel you need to seal it in some way, do not seal it 100%. Leave an inch or so not sealed at the back where it is not noticeable, that way it will look good and water can get out if need be.