This process style seems to fit most of the organisations which we have worked with.
There ARE processes, and where they exist, they are important. They describe how things get done, who needs to be involved, and provide a way to measure the effectiveness of the business. But to pretend that this can describe everything that a business does is just plain wrong.
So try modelling your processes this way.
Look for the events, even if they aren’t neat, software based events but are emails or phone calls from one part of the business to another. Just understanding these events can give really useful insights into the real dynamics of a business. And you also discover some textbook processes which happen as a result of the events, even better.