Your link appears to be the specifications for the old band - there's no barometer listed in the sensors, and there are dual batteries listed (I believe the new one only has one).

I wish there were a better distinction between the two; this should be called the Band 2, not the "new Band." This is made worse by the fact that your link is reachable by clicking "Support" -> "Hardware" -> "Microsoft Band Specifications." Nothing in that path suggests anything about the old Band.

The specs for the new Band are at https://www.microsoft.com/microsoft-band/en-us/features - you have to click on "tech specs." This supports the -300 to +4877 meters number.