Does hard reset downgrade device? I just "repaired" an iPod Touch, 4th generation (MC540BT). A friend of mine didn't use it for a year because it didn't charge. After playing with it a little; I finally managed to turn it on and it worked. She (my friend) told me that it didn't work as soon as she updated it to 6.0.1 and asked me if I can downgrade it to the previous version. I told her about hard reset but I want to know if hard reset brings it back to the iOS version that it left the factory with.

In less words:
Does a hard reset downgrade device or allow me to downgrade?
No - If by hard reset you mean 'restoring', it will restore the device to the most recent version of iOS that is able to be installed on the device. Restoring will only let you install the last version—there's no choice.