The government has really strict standards for alcohol content because of taxes, and companies would certainly not give away extra product, so we should review the instruments and procedures we used for testing that bottle. In my experience testing alcohol is a very finicky process and you have to be incredibly precise. This is the tedious side of science.
First thing to always check is the temperature of the sample as it will greatly swing your results. Here is a calculator that you can use to correct your proof based on temperature. You will always need to measure 3 out of these 4 to get an accurate "gauge" of your spirit: Temperature, proof, weight, volume.
Weighing the spirit is always the most accurate way to determine the volume. All good glassware in the lab will tell you what temperature it is calibrated to for water, but alcohol expands and contracts more than water does so you can't get an accurate volume reading unless you are spot on with the temperature. It is possible to use weight, volume, and temperature together to determine your proof too.
The federal government put together this video series to show the legally acceptable methods for testing. The lab still testing has to be super accurate by volume. It's good to run practice batches multiple times to make sure the technique was correct as even 1 ml can change your results. I always asked the lab tech to double check my work, and we would run a batch at least twice before we packaged it just to make sure.
There is a free phone app called Hoochware (available on iPhone and Google) that has a bunch of calculators that you'll need.
To double check your results you can dilute the sample and test it again. Be sure to use a proofing calculator since the volume math is not as simple as 1+1=2. Also good to note that combining alcohol and water will generate heat and you'll have to keep an eye on the temperature when measuring after mixing.
It might be worth it to spend some money on a high quality hydrometer set (or just a couple in the most important ranges, say one 70-90 proof and one 180-200 proof) and an accurate thermometer so you don't have to spend so much time running the lab still.
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