That certainly isn't what the people of Kashmir want.
Not quite.
Azad "Kashmir" was carved out of the Jammu region...the people speak Potohari/Mirpuri and Pahari, not Koshur.
The people of Kashmir would prefer independence in some ways...but if it came to only two options, Pakistan would certainly get the nod over India and the raping, killing army.
Maybe Azad Kashmir was carved out of Jammu but there are many people in Kashmir valley who are linked by relation and culture to Azad Kashmir.