We agree on the correct reading - my take is just that there is a different reading that could be argued.
Imagine you were in the world of OOTS and saw the text of Antimagic Field and someone pointed out the argument that I made - would you want your first test of the field to be in battle against a spellcasting undead to be against an epic level sorcerer Lich or would you prefer to find some low level undead spellcasting creature and run a quick test first to just rule out the potential reading.