Let me see if I can restate what you just said. The major conceptual difference between state machines and FBP is that FBP could have output from one state potentially go to more than one state at the same time. State machines, ordinarily, cannot.
Personally, as I never studied state machines in school (as such), but learned about them on the job, I never had that restriction on them. Why would that restriction be placed?
Now, I'm thinking that another way to look at it is the difference between procedure-based analysis and data-based analysis. State machines are more concerned with the actions that can take place. FBP is more concerned with the data that is moving through the system. Right?
We are the carpenters and bricklayers of the Information Age.
Don't go borrowing trouble. For programmers, this means Worry only about what you need to implement.