Sorry, no, exactly the opposite of what you are saying. What it means is that if there is a fault that Hyundai determines to be the result of non-authorised parts then the warranty will not apply to that fault.Read it again...this confirms exactly what the dealer GM said - by using 3rd party stuff (" defects attributed to the use of non genuine parts and accessories" , you risk your warranty protection. That would seem to be quite clear.
It does not mean that the use of non-authorised parts voids any warranty in itself, which is what you have been saying.
Even if Hyundai make that determination, they have to justify it by demonstrating how the non-authorised part was responsible for the fault, or their decision can be challenged and would likely be overturned.
As said before, it is nonsense to suggest that fitting a new, non-OEM, radio would void the warranty on any part of the car. It is only if and when that non-OEM radio causes a fault elsewhere in the car that there is any risk to the warranty protection on that component, rendered faulty by the non-OEM radio. Realistically, that would not be a likely issue because other than such things as speakers, amplifier, cabling directly related to the entertainment system, and dashboard mounts and bezels, there isn't much that the non-OEM radio could damage.
Your supposition that the OP in this thread is doing a disservice to Hyundai owners by showing them how to replace their original entertainment systems is similarly nonsense.