My son is 4 months old. For the first few months, 12 changes a day was definitely not an outlier. However, we were very quick to change his diaper once we noticed it was wet.

$1000/yr for diapers is definitely possible. You and I may have the luxury of purchasing diapers in bulk, but for many people (such as the young woman in the article), 32 diapers for 10 bucks is reality.