If you think of the hardware as a black box, it does correspond to the instruction set architecture presented. Generally you don't think about implementation details of an op-amp when you wire it into a circuit. The issue is that CPUs have become so complex that the lines are blurred, since the external interface is so removed from what's going on inside with micro code and ooe and cache. So while pedantically there are no longer low level language outside of microcode, that renders the term useless, and I'd prefer the natural language evolution that's occurring.

> actually believe that there is a straightforward correspondence between C code and what the machine is actually doing, which is wrong.

That really depends on your definition of "the machine". If "the machine" is "hardware", then sure. But if software is a considered piece of logic onto itself, that, when pitted against a sound model of an architecture will result in a series of logical steps, it's different: there is a very straightforward correspondence between the model-machine and assembly/C. Whether there is a 1-1 correspondence between the model-machine and any accidental hardware it is implemented is not that relevant.

So if low-level is defined as the lowest level that any hardware abstraction functions exactly as its logical function and not its silicon, it tells you exactly what the machine should be doing, even if it's doing it through different means.