I have purchased many of my Apple products Refurbished. They are like new, have the same 1 yr warranty as new, and save you some decent coin.You can even purchase Apple Care on them, like new products.
My Airport Time Capsule is now going on 3 years, refurb. My Apple TV3 and AppleTV4 are still ticking without a hitch. I have bought Macs, iPads, Apple Watch, and accessories refurb without an issue.
I can't say enough good things about Apple's Refurbs, not so sure about other sources like you see on Amazon for example.
My understanding is, Apple gets returns from customers who buy something, try for 30 days, and return. Often, purchases made right before a new release come back in favor of the newer model. They seem to wait for a stockpile of items, put them through the refurb process and sell them. So, they are not always available, but since the 4K model just arrived, likely they have a number of the ATV4s coming back to swap to the new model.
They also will take a failed device (in 1 yr warranty period, or through Apple Care) and essentially remanufacture it and sell it as a refurb unit. I suspect more care goes into the refurb process than new products as it is not likely to be a full assembly line operation.
Every electronic device has a certain failure rate, so there is likely as much chance of a new device failing as a Refurb.