To be honest, I thought there were some very bad calls, or rather non-calls in the NFC game. Particularly on the Cardinals last drive, I saw a lot of holding and illegal blocks. But it's very hard to say if here was any conspiracy or not, and there is no evidence.
There's very little reason for the NFL to allow anything like that to happen. Pittsburgh is not a big city and neither is Baltimore, yet they both got into the AFC championship (Smaller towns = smaller ratings.) Phila. is larger than Phoenix or at least the TV market is, but if there was a bias, it was towards Phoenix, IMO.
Off hand, i would say that our tendency to want one team over another tends to magnify our perception of calls that go against our team and to minimize the calls on the opponents. It's very hard to keep subjective bias out of how we see things.
I think all the sport leagues understand the importance of games being called fairly, far too much is at stake for a conspiracy to actually occur. Any solid evidence of an attempt to manipulate the outcome of any game for any reason has the potential to destroy the league! No one will pay to watch a crooked or fixed game. It goes against our sense of what is right and just.
Lots of people say that there is a bias in sports and for certain players in some leagues it certainly seems that way, but there is no reason to prefer a Pittsburgh win over Phoenix that could possibly justify the NFL intervening or allowing someone else to intervene to affect the outcome. Even the fans in the winning city don't want their victory to be tainted in that way, no matter how badly they want to win.