Forbidding tivoization does not forbid running the program, it forbids embedding the program in some piece of hardware and then not providing a means for the en

Forbidding tivoization does not forbid running the program, it forbids embedding the program in some piece of hardware and then not providing a means for the end user to run their own modified version on this same hardware. If a TV is to use some GPLv3 program, then it must allow the user to replace the program with their own version. And yes, tivoization is a major reason why GPLv3 was written indeed, it was seen as a loophole to fix by the FSF.