Your theory has two problems:
1) How precisely do you know the position of the sensor itself? If the robot moves, you will likely have more error than 1 cm.
2) The occupancy cell math calculates a probability that there's something in a particular cell. If the beam scans the cell stochastically, then when you get a hit, you need to update the cell with a probability greater than one (!) based on the ratio of the cell area to the area covered by the sensor. Each successive stochastic scan of that cell will then successively approximate the occupancy of the cell.
Note that you have to choose both sensors and filter characteristics to match the desired application. If you want 10 cm cells and your beam width is 1 cm, you either have to sweep each cell multiple times each time you scan it, or you have to average out more scans, to get a good measurement for the cell. Note that this is a beam width vs cell trade-off, and the size of the object doesn't matter as much in this case.