As I mentioned for gas and electric standards, you could probably say "certified to NSF standards" for non-commercially-integrated (homebrew) cookers and maybe get a little slack. But then you'll need to learn and follow these standards, in particular NSF/ANSI 4 which applies to cooking equipment. This is not unlike building your own home...you can do it but you certainly need to fully understand and follow the Universal Building Code and National Electric Code before you invest in materials, time, and before calling out an inspector.
As JJ said, that brick is a problem. For starters, you'd need to cover the top and sides with continuously welded stainless sheet (something that can be regularly wiped down with disinfectant.) You should verify that exposed brick in the cooking part of the chamber is allowed, which I think it is, but again I know nothing about restaurant regulations. This is not a family, church, or scout fundraiser you're considering embarking on.
I agree from a fire safety standpoint, the picture you provided looks ok...that's what the building spacing and combustibility comments were addressing.
But this is not portable, at all. Any outdoor cooking establishment I'm aware of stores their equipment, off-hours, inside a normal restaurant environment, away from stray animals that can urinate on it, etc.
I think the building dept was doing you a favor. Ultimately it's the health dept that determines these sanitation requirements. I'm completely flabbergasted that anyone from a US county health dept said it was fine.