All I know is that if you want a finished 1" board when you're done, you better mill it at 1-1/4" so it leaves you room to plane to thickness.
Myself, for my purposes, I mill at 1" and let the chips fall where they want. I have a board somewhere between 7/8" and 15/16" when it's done drying. I build with only rough cut so serves my purposes fine.
I'm also not too picky about how my boards look. They're mostly flat and square and hold up buildings and things. Can't ask for much more, can I?