A: Yes, and it increases with depth the further underground you go. A good way to think about atmospheric pressure is to realize that, here on the Earth’s surface, we are at the bottom of an “ocean” of air. If you go underground, perhaps into a cavern, you add an additional depth of air, just like you would by diving deeper into a pool of water.

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this from usatoday http://www.usatoday.com/weather/resources/askjack/wfaqpres.htm
I can’t find much else online. maybe it’s hogwash?
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Maybe he’s using a barometric altimeter, which ties into GPS coordinates to calibrate expected height at their current position, and figuring they aren’t in a sealed underground chamber with unusual excess pressure.
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Maybe he’s wrong
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Maybe he calibrated his barometer at sea level before entering the perfected air pressure of his fallout shelter, and used amazing SCIENCES to calculate subtle changes over time.

… basically I just thought of a barometer as magic tube of mercury that tells you your height. Wasn’t really aware of the problems weather causes. feel like a redneck idjit. but. the point is that one of these brainy Dad’s feels he’s worked out a reason to believe they aren’t ridiculously deep underground. good enough for my science fiction.

(cringe)