My radio 9 always did that, I dont know why.
I have since replaced it with an AVIC-Z3, which needs to turn on to boot up, so it doesn't matter anymore, but here's the thing.
When you look at the key switch, there's the following positions:
OFF
I
II
(start)
Well, the installer told me that position 1 wasn't wired to the radio, in fact, there wasn't any wiring going there at all. Thats just weird. Why wouldn't there be wiring there for turning on the radio when the car wasn't running?
I don't know if that helps, but maybe that has something to do with why some radio 9's always come on when you turn the key on.