Why is my iPhone trying to download a software update I already have?

I'm trying to restore my iPhone, but in order to do that, iTunes keeps telling me I need to have my software updated to iOS 6.1.2. The issue with this is that I already have this update and I don't know why it won't let me restore my phone without installing an update I already have and have had for a while now. I tried downloading it anyway, but it said my network timed out. I tried going into my settings and searching for any software updates there, but it wouldn't leave the "Checking for update… " screen even after waiting for around 10 minutes. Can somebody please help? I'm starting to get really frustrated.

It always says that you need to update your software when restoring, even though it's already updated. So that's normal. About the 'network timed out'-thing, that's not something that's wrong with itunes/your iPhone, it's your network. Try downloading the firmware from here and see if it works: http://www.felixbruns.de/iPod/firmware/, just select your iPhone model and download. Then just hold shift(or alt on mac) and press "restore" on iTunes, a window will pop up allowing you to choose a file, select the ipsw file(the file you downloaded) and just restore as usual.