Hi, I've used a FuelBand (SE+) for a year or so.
They do log / track locally. There is enough onboard memory to store several days' worth of activity, in one minute increments as far as I can tell. (I only sync my data once a day when recharging by USB, but I've often gone a few days between. All the data make it home.)
Moreover, the FuelBand has a display that gives real-time feedback: it can give you move reminders if you've been still for too long, or "encouragement" if you start up. (I've disabled this feature on mine.) It makes a little animation when you've hit your daily goal. You can press the button to get statistics on Fuel (more on that in a moment), number of steps, and number of "hours won" (hours with at least several minutes of continuous activity) at any time in the day.
So yes, there is local storage, tracked minute by minute, accessible on demand for visual feedback. It can communicate via Bluetooth with an Android phone or iPhone for a bit more capability. (The button broke on my FuelBand, so this is my sole means of real-time communication with the device.)
I'd imagine that where they might have had more trouble is the "health" than the "tracking". They use an arbitrary unit called "Fuel" that correlates well with physical activity, but tries to scale many types of activity onto a single unit of measure. I've noticed that on very inactive days (couch potato sick day), I'm under 1000 Fuel. On a moderately active office day where I take a walk in the afternoon, 2000-2500. On days where I go for a run, 4000-5000+. It seems to scale well. But they may not have enough trials and other tests to validate that tracking Fuel means tracking health.