Just a question for you, what is "fatwood"?
I personally won't use anything but good seasoned hardwoods, including kindling for 40 years and have never had an issue. If it ain't broke, don't fix it. If you really want to know call your insurance agent, he or she will give you their OK if it's a safety concern. If they don't have any concerns then you are good to go, of of they do well then they have given you a definitive answer.

I bought a wood burning stove a few years ago and the dealer said don't ever put fatwood in it because it burns too hot. That is the only thing he said not to burn. He said that I can fill it so full of wood that no more will go in though.

I have a wood burning insert, and I use one small piece of fatwood as a fire starter. It is incredible how well it works. Everything I could read basically said one piece per fire should not harm anything. I am curious as to what others think.

Fatwood is just really pitchy pine.
It is fine to use one or two (or other better things like super cedar fire starters) to get a fire going, but no more. Too much pine makes for sticky, dirty residue in your chimney.

And burning hot is good- it keeps things clean.
Please refer to your owners manual for a rundown of optimum burning temperatures but know that hot is good and a slow smolder is terrible.

I always ask for a report on how my liner is looking after my annual cleaning. I am also handed the bag of what was removed so I can adjust my burning techniques.
I hardly ever see more than a couple of tablespoons of ash and that is because I burn hot and only use wood that have been very well seasoned.