well no, the browser adds them when it loads and parses it for rendering. the inspector just shows you what the browser created. the same is true for all browsers, their inspectors will reveal how the DOM looks like for the browser.
If we're discussing semantics here, when a browser parses it for rendering what would it mean to "add them?" After all, the HTML is only a textual representation of the rendered DOM tree. I think it's perfectly valid to say the inspector is adding them in, since the browser doesn't really bother to adjust the HTML if it can already parse it.