It's not that the laws of physics themselves use different descriptions at different levels

I think cases could be constructed in which they do. Assume we live in a world where the basic physics are cellular automata, the game of Life, for example. Then there would be the standard laws, specified at the level of individual cells. At the same time, there would be laws defined at the level of higher-level structures - gliders, etc. If the initial configuration was chosen carefully, these laws could be completely sufficient to fully describe the evolution of the world. Then, there would be no reason to suppose that the "basic" (low-level) description is any more fundamental than the "emergent" (high-level). In fact, it can be argued that the reverse is true, if the low-level configuration was specifically chosen to make the high-level one possible.