Yes, it's all about storage requirements. If they don't fit in a case box, the organizers have to put them somewhere else. And then make note of the extra bottles. And then make sure everyone who handles the beer knows where to find the extra bottles. And then hopes that nobody breaks them because they can't be stacked and stored like the other ones.
You probably don't know how many different people have to handle the beer once you've shipped it. Unpackers, sorters, box movers in the receiving location, moving them for transport to the judging site, moving them to the judging room, stewards finding the beers, judges opening them. For the NHC, you're talking about 2-3 pallets of beer. If your beer doesn't fit, basically everyone in that process will be cursing you.
Your beer is more likely to be lost, broken, or mishandled if it doesn't fit. I've seen people invert bottles to make them fit in case boxes. Not really the handling I'd want me beer to have in a competition.
So if your beer is oversize in some dimension, it might or might not work, depending on the other entries. If it's too tall, it will never work. If they put it in the box, you will likely have it be broken when the boxes are stacked. If it's too wide, it might not fit in the box, unless the adjacent bottles are smaller in size and the case dividers are flexible. How do you know what size the adjacent bottles are? You don't. So if you use a bigger bottle, it might work or it might not. If it doesn't and it's too big, then you lose.
I'd say if it's close enough (few hundreds of an inch), then you are likely to be OK. Unless everyone uses them, or at least those in your flight. It's a risk, but probably a low one. But it's a risk you have to be willing to assume.