I guess you may be just a bit confused about the way Illustrator displays dimensions in the Transform palette.
Let's take the green western boot in your example file. Its width is 0,7884 cm and its height is 0,8855 cm according to the Transform palette. If you rotate the boot by 45 degrees for example, the Transform palette says that its width is now 1,0451 cm and its height 0,7705 cm. But that does not mean that the boot dimensions have changed. It just shows how Illustrator's Transform palette reads width and height based on a (virtual) unrotated bounding box. In other words the values you see in the Transform palette are based on some kind of Cartesian coordinate system with horizontal and vertical axes.
That is, at least if my guess applies, you don't have to worry about it. It's just normal and you can be sure that the rotated boot has not changed at all.