Perhaps it is not me who does not understand.

I will try to explain better.
1/1000 of an inch is more than two and a half times larger than 1/100 of a millimeter. That means a measurement to the nearest one hundredth of a millimeter is over two and a half times more precise than a measurement to the nearest 1/1000 of an inch.
This means you can take a measurement of 13.03 mm and convert it to inches while maintaining the same precision and accuracy you would have had if you had taken the measurement in inches to start with. However, if you convert from thousandths of an inch to millimeters, your answer is only precise to the nearest fortieth of a millimeter, rounded to the nearest hundredth of a millimeter, which is less precise than if you had originally taken the measurement in millimeters.
To test this with your calculator, convert 0.001 inches and 0.002 inches to millimeters. Notice that the difference between 0.001 inches and 0.002 inches is just over 1/40th of a millimeter (about 0.0254 mm) The difference between .002 inches and .003 inches is about the same, as is the difference between 0.003 inches and 0.004 inches, and so on. This incremental difference is larger than the incremental difference of a metric caliper that reads to the nearest 1/100 of a millimeter so it is less precise than if you had originally taken the measurement with such a metric caliper.
Now convert 0.01 millimeters and 0.02 millimeters each to inches. Notice the difference is about 0.00039 inches, or about 1/2540 of an inch. This incremental difference is smaller than the smallest incremental difference obtainable with a caliper that only reads to the nearest 1/1000 of an inch. Even after rounding to the nearest 1/1000 of an inch, the result is still just as precise as it could be had the measurement been initially taken with caliper measuring in thousandths of an inch.
Thus it is better to take your measurements in millimeters with an accurate, quality metric caliper, since the same number of significant figures offers more precision.
I'm not a cue maker, but I'm certainly no stranger to taking accurate, precise measurements. I know many cue makers are perfectionists. I thought maybe some of those perfectionists, possibly including the original poster, might appreciate the information. I'm sorry I didn't state my point clearly enough to be understood the first time. I hope this is better.