To see what happens with the std lib version,
go build && ./yourbin
Go to http://localhost:8080/ (make sure you force refresh if done in browser) and notice that the response header is OK:
Last-Modified:Tue, 09 Feb 2016 05:08:20 GMT
Now run the GAE version. You can't test this in dev, so you need to push it to prod.
It can be seen by going to http://gae-test-1133.appspot.com/ (make sure you force refresh if done in browser) and notice the bad header:
Last-Modified:Thu, 01 Jan 1970 00:00:00 GMT