Yes. Your box of 1 inch correlates to 1 3D unit in any 3D modeller or engine. Not just DBP. I can open it in UU3D and Milkshape and both of them display the 1 inch cube as 1 unit long.
You .X file is an ASCII .X which makes it easy to look at what is actually stored. Because of the writing on the cubes there is a huge amount of data, but if you look at the end of the 1 inch cube frame data, you have a bunch of entries which correlate to it's extremities. e.g:
38.87107849121094, 1.001000165939331, -0.49899986386299133;,
38.87107849121094, 0.0010000815382227302, -0.49900001287460327;;
The cube is at approx 38 on the x axis. Then you can see it's lowest point on the Y is almost zero, and highest is just over 1. On the z the lowest is -0.5 and highest is probably 0.5.
So the cube is 1x1x1 ish in the file, so all 3D programs will open it and make the 1 inch cube 1x1x1. From that you can conclude either:
a) Every 3D engine/modeller is in imperial, or
b) They're simply interpreting the data in the .X file, and it's Inventor that is choosing to save a cube that it defines as an inch as a 1x1x1 file.
It's up to you. I am going to plump for b.