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How is it not true? If you know asm, you know your CPUs external documented interface. You should also learn about your platform and how other interfaces work.
Of course, on modern OSes, the bulk of the code is usually usermode code which is isolated from having to deal with hardware directly.
The other step in learning how a CPU works is to learn how CPUs are designed and how they work, and maybe make your own as an exercise (buy some FPGA to run it on). You may also model a software emulator which emulates your entire platform. After that, you can say you truly understand how computers work.