There’s more to it. The philosophy behind the architecture (functionalism, simplicity, and keeping the raw material’s appearance instead of hiding it) maps very well to a philosophy of web design. The main difference is that “raw” now refers to (roughly) the HTML code rather than concrete. The other points, simplicity and the utilitarian character of the layout and of the underlying code, and buttons that look like buttons (analogous to doors that look like doors) are very similar.

In contrast, “flat” is just a visual style.