> The fact that my headphones need a AAA battery
Just because some headphones do not need batteries says nothing about these specific headphones being talked about. Both can exist at the same time (a pair that requires batteries, and many that do not.)
For example, Bose Noise-Cancelling Headphones, which are quite popular, require AAA batteries:
http://worldwide.bose.com/productsupport/en_us/web/qc15/page...