Throughout the movie we see ash in the atmosphere. First of all it doesn't come down clumps like that, ash is a fine powder (Mt. St. Helens is a good example of this). Secondly, If ash was falling like that, they would have to cover their faces, otherwise they would die from inhaling it.
You are right. The condition that you are talking about is called Black Lung or also known as pneumonoultramicroscopicsilicovolcanoconisiosies. It's in Guiness World Book of Records.