I agree with you–when I’ve purchased a refurb product and had something stamped onto let alone engraved into the product boldly indicating the refurbished nature, it’s always bugged me, making me feel somewhat “branded” as having a “cheaper” product or being cheap (even when the item might be in a case). But I understand why the companies do it, including to prevent warranty claims that might not apply as with brand new products.
My recommendation here: get a case so that the engraving is out of mind and sight. And to protect the case as well.
Hopefully the player will be problem-free for you. No way to know why it’s a refurb–I had a long period where every refurb I purchased was as good as new, and I had the impression that manfs. were selling new product as refurbs simply to set up a new distribution chain at a lower price-point, trying for another line of customers. And then I purchased a refurb Magellan GPS unit, only to find, when I got home and opened the box, that it was covered in watery dried mud (I later returned to the store and swapped it for another, getting a unit that again looked as if brand new).
From what I’ve seen here, use and keep an eye on the player right away, to make sure it’s fine–where I’ve read here of refurb issues, the issues often seem to be there right away (and if that were to be your case, you could return the player in the first 30 days).