Cannot Upgrade jailbroken iPod touch 4.3.3 to iOS 6.1.2
I finally resolved this. It turns out I had 6.0 (I didn't know because my friend was the one who got it and Apple isn't signing it anymore). I downloaded 6.1.2 and then my IP got blocked for too many requests. So I used a VPN for verification and then it worked.

So, like @Chris A said; You don't need to do all that TinyUmbrella crap (unless you're downgrading). If you have the current iOS offline (like in my case) or updating to the recent firmware, it'll work just fine.

Thanks to all that stared at my question.