If your boot sole fits in the footbed it's pretty much a go. The burton straps on the mediums can easily be adjusted (just like any other binding) to accommodate a larger boot. The only thing that doesn't move is the width of the footbed and the heelcup in their case, but that would be solved by off setting the binding more towards the heel edge.
The reason why someone would go to a medium and not a large binding when their foot size overlaps both, would be so that they can go with some of the smaller boards (waist width wise) and also get a tighter fit in general.
Depending how large your boot really is, you may have to always make sure that no snow is in your binding when you strap in. This is something most riders do anyway, but if your fit in the medium is hella tight and just right, you will have much less leeway for potential frozen snow jammed in the binding.
I remember seeing a video that explain this all, but I can't find it.