The problem is due to Site collection Quota exceeding the allocated limit. I found this issue when I tried to add a Secondary site collection administrator and Central admin reported this error.
Your changes could not be saved because this SharePoint Web site has exceeded the storage quota limit. You must save your work to another location. Contact your administrator to change the quota limits for the Web site.
I went to Central Admin -> Application Management -> Configure Quotas and Lock
and increased the site storage limit. After doing this sharepoint was able to open the document in edit mode. It's really strange that sharepoint doesn't log error when user tried to open the word document. And another side effect of site collection exceeding storage limit is that if you try to add an site collection administrator in Web Application (Users & permission -> Site collection administrator) is SharePoint will display a blank page if you add user and click the Ok button.
I was completely deceived by this error and started looking at some of the blog which closely matched the problem that I faced
Hope this helps someone.