Personally, I'd have a problem accepting something advertised and sold as new if it looks to be an obvious refurb, return or demo. You could spend that month testing and not finding any problems, only to have it possibly break down after that time and then you'd likely be upset for having to pay to ship it in.
This is not the way a shop should be doing business IMO, no matter what the excuse. This is the kind of thing that would make me want to make an unboxing video of everything I bought with hi res cam to reveal any scratches before use. Threatening to put something like that on YouTube would no doubt have them quickly jumping through hoops for you.