I should have phrased that differently. The lungs don't shrink because they're filled with high-pressure air, but shrinking wouldn't damage them. "Crushed" implies damage and it was the wrong word to use. Lungs are soft and effectively can't be crushed, the way that a balloon can't be popped by deflating it.

The guy with the world record for free-diving had the air in his lungs squeezed to a twentieth of its original volume, but lungs are built for that sort of thing. Simply going from inhaling as much as you can to exhaling as much as you can reduces the volume of air in your lungs to a fifth of its original volume, a much bigger absolute change.

(He still had to practice and prepare for years, and he was probably born with an exceptional natural aptitude. Don't try this at home!)