As far as I understand things a nearly new phone is just that.
One that's been out and returned within the 30 day cooling off period and then checked by Vodafone to ensure it's been wiped of info along with the original Apple ID and is of a satisfactory condition.
This does not always include original packaging.
Vodafone do apply a 2 year warranty and so does Apple now. Apple.com/legal/warranty/products/warranty-edition-row-english.
I agree Vodafone need to be crystal clear when advising on what a nearly new phone is as this shapes the final decision by the person contacting them.
Vodafone can send a returns bag to you which should be free postage as your cancelling within the 30 days cooling off period.
My own decision would be to take it back to a store and I appreciate the distance you'd need to travel but for me the peace of mind of knowing it's back in Vodafones hands to speed up the process is paramount for me personally.
I wish you all the best with this situation.
Current Phone >
Samsung Galaxy s²³ Ultra 512gb Phantom Black.