I personally feel any chef who has full responsibility for his or her outlet or operation including administrative, bottom line, P&R, all paperwork etc should carry the Exec. title. A working chef should carry production.
Being certified does not always reflect the position you currently have. A CWPC can work Exec. Pastry Chef, Food and Beverage Managers etc. I know.
Nothing wrong with titles! Most people work hard for them. Sometimes its the only reward besides the customers.
I somehow have gotten a jacket that reads Chef/Owner. I chuckle when people ask me about it, I tell them I own a stable of chefs.
Just my 2 cents.