I had one app that updated for iOS 7, but it was a new app. My old one quit working. It had been a free app. The new one became a paid app, so I no longer had it. When I attempted to download it, it asked for my password. Anything I download from my purchased list do not ask for a password. Some older apps may have updated and require that. Makes no sense though. Does it ask to pay for it?
I think this changed in iOS 6 or 7 when the cloud logo appeared next to apps that were already associated with your Apple ID. Before this, you'd have to enter your password for everything. Sounds like the OP got to the root of the problem here... Although a bit more of a hassle, I'm never nervous when my phone asks me for my password. It's a great security measure.