Why isn't the dimensional data useful? It determines what you can fit in the box.
No, the reality of the box determines what you can fit in the box. The dimensional data has no effect on the box or what you are putting in it.
If I'm asking for a box, I'm not asking for a truth or a belief, I'm asking for a real existent object that really exists in real objective reality. That seems to me something with objective existence that needs to be talked about.
Note that the only way you could introduce this "what needs to be talked about" into discussion was by starting it with "if I'm asking for a box," which you aren't. We aren't even talking about a box. There is nothing here with any objective reality at all.
IF...
we were both
looking...
(note that objective reality is interacted with not by talking)
for a box to fit our stuff in...
by the time you reached agreement with whoever had your box about how to measure it...
(inches, centimeters? LxHxW, or WxLxH...wait, my TV is measured on the diagonal! what precision, will give or take half an inch do, or should I be more careful? is your tape calibrated? how reliable are you? do you have actual experience using a tape?)
I will have taken the objectively real box and stuffed my objectively real junk in it to see if it really fit or not. That's how objective reality works.
All the agreements, all the language, all the measurements and truths and beliefs...none of them even exist in objective reality. They have no impact there, and objective reality has no interest in them.