I don't know, that page seems a bit ambiguous to me:
> New: Just like it sounds. A brand-new, item. Original manufacturer's warranty, if any, still applies, with warranty details included in the listing comments. Original packaging is present for most New items but certain items like shoes may be re-boxed.
> Used - Like New or Open Box: An item in perfect working condition. Original protective wrapping may be missing, but the original packaging is intact and in good condition with minor damage possible. Instructions are included.
Reading those two descriptions, and considering a brand new, never used item, which has had the box opened and then the items re-packed into it as they originally were (in perfect condition, in their original wrap, unused, no fingerprints, etc.), I would definitely consider that "new", not "used - like new". As a buyer I would also have no problem receiving such an item.