"Technically" publishers could do the same thing with a Wii game. All you need is a unique identifier for the machine (friend code), a unique identifier for the disk (which might be more expensive to do but isn't impossible), a server to keep track of which machine is authorized to use which disk, and code in the game to check in with that server before it does anything else.
The difference here isn't whether or not it's possible to set up DRM, it's how difficult it is to set it up, or not set it up. If publishers want DRM on their PS4 products they have to go through some effort to implement it; there is no DRM by default. Xbox One, on the other hand, has DRM already set up for them, whether they want it or not. I haven't read anything anywhere saying they have the option to disable it. The closest option publishers have to a DRM free game on Xbox One is to allow the game to be resold (through an authorized reseller only, of course) and even that is not enabled by default.