I ran into an interesting problem where someone was not able to open up a Google Doc without having to log in. I was not able to recreate the problem with any of my browsers in or out of “private” mode. I did some searches and I found that there was a similar problem back in 8/2011, on the Google forums one guy said:
Oh no! This is still ongoing. The post by Bas Braams explains why it’s not universal: if I try to access the documents in Chrome, Firefox, or Safari, I’m required to sign in first. Unless, that is, I delete cookies. Then it works the way it’s supposed to.
I had her try in a “private” window so that it shouldn’t look at her cookies. That worked perfectly. I then had her delete all the Google cookies, close, and reopen the browser; the document worked fine. We cleared the cookies on Safari on her iPad and that worked as well.
So it seems that there are still issues with Google Docs and cookies. Try to open the doc in a private or incognito window to see if that works before clearing out all Google related cookies.