for the record, all iPods are made by Apple, yours was just sold to you by HP. i can't see any reason those iPods would not qualify.
from Apple: A free iPod recycling program, conducted through Apple’s retail stores, offers environmentally friendly disposal and a 10% discount on the purchase of a new iPod.
doesn't say anything about who you bought it from; as long as it's an iPod, they'll take it.