Some products advertised on RefurbMe are certified by Apple, others aren't.
RefurbMe partners with several refurbishers, including Apple. While other refurbishers may sell refurbished devices in varying degrees of cosmetic condition (Excellent, Good and Fair), Apple sells exclusively grade A refurbished products like these:
Apple-certified products are in near-mint condition. No scratches, no scuffs, and they come in the official Apple packaging. However, bear in mind that Apple-refurbished devices are more expensive than products sold by independent refurbishers.
If you are only interested in buying an Apple refurbished product, learn how to filter results for Apple Store products.