That looks like the same page to me, but with different stylesheets attached. If you're just re-displaying identical HTML from your local server, the relative stylesheet paths in Google's HTML would no longer be correct. Also, any AJAX requests meant to run after the page loads would no longer work (both because the relative paths to the scripts would be wrong, and also because Cross-Site Scripting restrictions would prevent them from contacting Google).
Attempting to scrape content from an AJAX-enabled application is no small undertaking. You'd have to replicate a lot of GMail's functionality to truly reproduce the exact page Google presents.