I can't decide if I think this is a bug or intentional crippling by Apple.
My third-party cable warns me, but works fine for syncing with my Macbook Pro, but won't charge.
If I plug the same cable into the charger that came with the iPhone it won't charge. If I plug it into a third-party charger with enough power to charge an iPad, it charges, though maybe a little slowly.
Before iOS 7, ALL of these things worked perfectly.
It's almost as if iOS 7 is more picky about the amperage or something, but it could be Apple being a bunch of jerks. 🙂