It was in earnest. What seems to be going on here is that we have a very different understanding of what "responsible for a flow of money" means.
In my mental model, someone who handles, protects, counts, transfers, etc. money to and from customers is fairly literally "responsible for a flow of money".
I suspect you believe your definition requires a higher threshold and/or type of responsibility that these roles do not entail, but I don't see where that is in your definition.
I think maybe you what you mean is that our hypothetical banker is independently making some decisions around how / where / etc this money flows with some degree of autonomy ?
My point here was primarily just to say that it is maybe a bit thornier of a thing to define than you realize given that your definition in my honest opinion and in what I consider a reasonable reading did not clearly leave out one of the primary categories of employee that you intended it to exclude.
Sidenote - stating that "you will find most people will agree with me" is an, um, interesting method of argument.