Please try first and after this comment.
I've done my downgrade on iPhone 5 and iPad 2 gsm and I've done it downloading firmware from Apple site and using Apple software and nothing more
As long as you will have proper firmware image downgrade will be ALWAYS possible.
I did just try it. iTunes won't install it because it isn't the proper build. This error happens because Apple is no longer signing anything but iOS 7. Just because you can download the IPSW doesn't mean you can restore your device to it. Downloading the IPSW is like being given a treasure chest that's locked. Apple will give you the key to open it. But after a while, Apple won't give out the key for older chests, only new chests. iOS 6 is an old chest that Apple isn't giving out the key for anymore. In the older pre-3Gs days, you could restore to any firmware, but no more. Only what Apple is signing. Why don't you go and give it a try yourself again right now. You'll get the exact same error as I and everyone else that would try to restore to iOS 6. There's no way around it. Millions of people know this. If you want to learn how you are mistaken, do some reading on SHSH blobs are how they are used during the restore process.