I have found the more accurately you reposition the tripod, the better the stitch will go. While software does allow you to adjust, I am finding myself tweaking the patch shot in Photoshop prior to stitching. I have had to take two patch shots at 45 degrees offset in an attempt to deal with tripod shadows. That makes stitching a bit more difficult. The final result is worth the effort.
You are absolutly correct that the most important part is keeping the camera level and at the same height. Positioning errors can be more easily corrected than height errors.
agreed - the more work you do at time of shoot the less work you do in post production. How many times have we all gone down that road? I know I have more than I like to admit.