The instantaneous error can easily be much larger than 15%.

Let's plug some numbers into a power calculator. Let's say that you're going 18 mph down a fairly flat road, assume some typical numbers for body weight, aero drag and temperature. All that the app has to work with is your weight, bike type, speed and approximate altitude (from which it can calculate approximate grade). Since it's running on a smartphone, it does not have access to barometric altimeter but let's assume that it can somehow measure your altitude to +/-10 feet.

If you're on the hoods wearing a flappy jacket (CdA 0.45 m2) and there's a 2 mph headwind, you're spending 210 watt.
If you're in the drops wearing a race jersey (CdA 0.37 m2) and there's a 2 mph tailwind, you're spending 115 watt.
If you're on the hoods and you're going up 2% grade with 2 mph headwind, you're spending 340 watt.
If you're in the drops and you're going down 2% grade with 2 mph tailwind, you don't need to spend any power at all, you can simply coast at 18 mph without pedaling.

2 mph headwind is so mild that you may not even notice that it's there,
2% grade at 18 mph is about 0.5 feet per second of elevation change. If it's just a bump in the road rather than a sustained climb, your phone will most likely fail to notice that it's there.

Now, if we're talking about _average_ power over the entire ride, then some of these factors are going to cancel out, and you might end up getting a work estimate within 15% of the actual value. But you can't, say, do intervals with this app because its measurements are going to be too far off most of the time.