Where are the weldments going once they leave your shop? I worked for a company that used to make train components for a German company and despite the fact that we were fabing them in the USA we had to hold to the German welding standard "DIN". This standard has a few requirements that I had never experienced prior to working at said shop. From what I am told when DIN is the standard, you are not allowed to grind any welds to meet the design spec or to change the size or shape of how the weld was installed. If the weld is over sized, had reject able discontinuities, or any other reason you may want to take a grinder to a weld, the whole weld must be removed down to parent metal and reinstalled correctly.
Outside of that the only other reason may be surface finish. Depending on what you are using to grind the welds flush to the parent metal it may be leaving course grinding marks that require extensive metal finishing to take out? Or the fact that if the parts are getting painted grind marks stick out like a sore thumb even under coats of paint, and if its a part that gets visually looked at on a regular basis the customer may not be satisfied with the results. Just remember if you grind it flush and leave grind marks the metal finishing will take your grind job into the parent metal just to remove for and example, rock wheel scratches.
I only throw these out there because I have had, and heard people say just about anything to get you scared into doing it their way. It may not even have anything to do with code, they could be quoting you that as an excuse just because they think it looks better that way. When it comes to motivating people some will tell you anything.
Probably missed the boat, but I figured I may take a stab as to why.