The way I always approach this problem is one of ownership. Congress, implicitly, assumes that individuals own their data. That is why it used to be possible to ask individuals to prove their identity by asking them to verify data they own, and presumably, haven't shared too broadly.
Identity theft is really a robbery then, because data which belongs to you is stollen. The government's opening position then needs to be that data belongs to consumers.
What isn't clear is the physical metaphor for what happens when you give your data to a third party, explicitly or implicitly. Am I 'leasing' my data to Facebook? Am I granting them shared ownership? Or is it more like a Bank... I'm allowing Facebook to "re-invest" my asset, they can make money off of it while they have it, but in exchange, they have to keep it safe.
I personally really like the Bank metaphor, and like banks, you can get certified as safe by the government to be a Bank, and have that certification taken away... We already have data protection rules like this in BTW, called HIPPA