"The design is the code" does not follow from the idea that design and construction are not separate things in software.

The thing to take away from that idea is that the design doc is not law written in stone, but a base for changes. It keeps your design honest on the high level. If you end up clashing with reality, and your design doesn't work out, you can backtrack to the design doc and refine it as necessary.

In short, the design doc should be a living document.