However, it is now mandated by the FCC that all barometer-carrying smartphones will report your accurate altitude information to 911 emergency response if you make a 911 call from your smartphone. So the location tracking element of the barometer is a very real concern for a lot of people, as it can tell a tracking company what floor of a building you are on at any given moment.
However I think it's quite clear that weather apps, and The Weather Company, are much more interested in the local atmospheric trends than they are about your current floor.
Edit: FCC citation: https://www.fcc.gov/document/fcc-adopts-new-wireless-indoor-...
How can this possibly be true? Wouldn't the pressure around a couple of square meters simply equalize instantly? You're not saying "within a mile" you're saying "to within 1 meter", and I don't get it.
The barometer is sensitive to altitude changes much much smaller than a meter, probably something like 0.1 meters. So if you are a person, with a smartphone, and you are in a tall building, the barometer can assist with determining which floor you're on. Other sensors would need to be used for calibration (since the changes weather will affect the floor-level) and it doesn't help with the x,y coordinates, just the z. But other location systems are now very very good at x,y and they mostly lack the z.
So by adding the high-accuracy relative altitude capabilities of the barometer to the existing x,y systems, you can get extremely precise locations.