Correct, but you have to consider the heat from the fire, it will kill most if not all chemicals (that part I'm not 100% sure about), any type of paper products do have chemicals in them. But any thing a person finds in nature as far as wood and un-processed lumbar is fine (boards and such, they are nothing but dried wood cut to form) is fine to use. Just don't use any pre-cut lumbar/wood that has a green color, that is more than likely "woolmenized lumbar" treated to withstand the weather. REAL bad news to burn.
That is how I just to get most of my wood ash from a spot that I always piled scraps of lumbar over the years when building things, I'd burn it and after a week I would get what ash I needed it also had a little soil from that spot included. Of course you must lime it good. It's always worked great and my plants always had a really good root system and they were nice and healthy.