Technically you don't "own" a device
As more and more devices have more and more semiconductors, which in turn contain their own embedded software/firmware, which you DO NOT own, only a license to use, so technically Apple have a point. If the screens are indeed counterfeit they're likely to have counterfeit firmware in the control circuitry.
Look at what John Deere tried with their tractors. Stopping mechanics or farmers tuning/repairing the vehicles because of copyrighted ECU code. The more software controlled semiconductors we get, the bigger this grey area becomes, unless everyone in the semiconductor industry switches to open source firmware, which in the case of vehicles will NEVER happen for safety reasons. And profit, of course!