You need to decide if you'll accept the criticism or dispute it. Does your state require a written, signed application? What about E-Sign/UETA rules?
I think the bottom line for me would be to ask for a cite, where I could see this requirement. I don't know otherwise that it exists. Next, you need to decide if you want to fight this. It needs to be resolved before your next exam. The board accepting the risk is support, but certainly doesn't resolve the disagreement with your regulator. You need to decide if you'll bump this up to an ombudsman or the next level in that agency's chain.
My opinions are not necessarily my employers.
Rules and Regs minus Relationships equals Resentment and Rebellion. John Maxwell