Uh, yes, China effectively demanded permission.
The real fact is that there are no rules regarding rules inside any ADIZ, so it is
YOU should stop making up sh1t.
Here are the rules China made for this ADIZ...
Announcement of the Aircraft Identification Rules for the East China Sea Air Defense Identification Zone of the P.R.C.
China effectively said that prior entering this ADIZ, there must be a filed flight plan, prepared for two-way radio communication, display of national colors, and complete compliance to all Chinese orders.
There are no exceptions. So yes, China effectively claimed this as territorial airspace, same as over mainland China.
Look at it from a closer to home perspective...
There is a sidewalk in front of my house. The sidewalk is public ground. If I begins to set rules on who can use this sidewalk, when can it be used, how can it be used, and finally for how long by anyone, I have effectively called the sidewalk territorial property, even though it is technically owned by the city and legally accessible to all.
China have done just that.