The point that the game was designed with the thought of a grid or similar setup isn't much of an overstatement, if at all. After all, movement, spell and weapon ranges and the like still were measured in inches, assuming 10ft (or yards outdoors) per inch. The wargame/miniatures aspect, and the assumptions of an official square grid over a hex grid are more than mildly implied.
3E makes a more rigid case for the grid as the only way to do things properly, but that tradition certainly has its roots in 1E.