Interesting dilemma really, it seems to me to be more psychological than technical in that they feel that ALL real estate in their building should be usable for whatever they want unless forced not to by specific printed rules rather than common sense. I have been in this situation several times, but fortunately for me as a consultant rather than an employee most of the time. So I could make my report and walk away when things got stupid like this (still sticks in my craw however just by remembering now).
How about this tactic;
From the sounds of it, they are not going to be able to accurately interpret the complexities of NFPA 70E (Arc Flash Safety), which not only can be interpreted to require up to 48" clearance on 480V gear, but also require a label on the outside of the box saying that anyone coming near must be dressed in a specific matter (PPE requirements) blah blah blah. I'm not saying here that this piece of equipment will require all that much, in fact is probably won't, but the complexities of Article 409 are too much even for some experienced engineers, let alone "non-technical types" with their heads up their ...
So tell them that as long as the person pushing that cart into the room or going in to remove it will need to wear a long sleeve cotton shirt, cotton underwear and fire resistant pants, they can do whatever they think is acceptable. Then show them an NFPA70E sticker example like this:
By the way, if it helps, NFPA 70E rules are very clear about whether the box is open or closed and will require at least 3'6" of clearance from any exposed live parts (implying Open) but adds "approach boundary" and "restricted space" requirements as well. Again, this applies to exposed live electrical equipment, but you can possibly exploit their likely ignorance or confusion by overloading them with this kind of info. For sure, there are scam artists out there now who are capitalizing on this to extract money from the uninformed, all you want is for them to not be stupid about storing stuff too close to electrical cabinets.