It seems when they say the NSA doesn't look into what Americans do, they mean no human has access without proper authorization. From TFA, a quote from an NSA spokeswoman: “All data queries must include a foreign intelligence justification, period."
Now, that's nice. Let's assume for a moment that's true - that's not saying anything about automatic collection of data, about computer analysis of such data, about how long data can be kept etc. "No-one is listening to your calls" is a complete red herring. It would be better if their methodology were based on purely human-conducted surveillance. That kind of work is expensive, and therefore must have a limited scope. What is apparently being built now is much worse than having some person listening to people's calls.
Everything we're being told is going on now just reeks of the Total Information Awareness programs which were, to some extent, supposedly discontinued. The goal seems to be the same - make it cheap enough to have total surveillance capability of everything anyone does. You can't do that with humans, but if you manage to build a computer system broad and smart enough, you can do a whole lot more. Humans aren't being phased out of the process because they present a larger risk to the population being monitored - they're just too expensive.
Fortunately, automated intel data analysis is still a very tough problem, but it seems clear a lot of work is being done to "improve" things in that field. That's not good news, it's bad news. Less human involvement in this context means less legal oversight and greater overall capabilities. You can't jail a computer system.