Easy question first:
If you want to use the backend are to edit your template files, yes you have to have, basically, wide open permissions. That said, you CAN always download those files to your desktop, edit them locally, and upload the changed file -- and you can also, edit them, and then ftp in and change the permissions back to something more secure.
For starters, that your db is not localhost has nothing to do with anything. Secondly, your site, IF its the one in your profile is hosted on pair.com. I KNOW that pair.com does NOT require your wp-admin to be 777 in order to function correctly.
You may be experiencing other issues that you have simply solved by doing that.
I suggest resetting the permissions back to something more sane -- 755, and figuring out the real problem.
You are right to be nervous about those permissions, and good for you for asking about their necessity.