D&D-as-toolbox is the game giving you the mechanics you need to run the game, and nothing else. You have the rules for making characters, running combat and leveling up, stats for monsters and treasures, and really that's all there is to it. Some elements, such as the nature of classes, spells, monsters, etc. might make an implication about the sort of game that the rules are best geared towards, but this is, at most, very vague. No part of the rules defines the setting for you, it's something you make up yourself. Take it for what you will that this is how D&D was originally created.
Which do you prefer?