Is Hubble's constant a property of the universe, or is it the mean value of the properties of many different celestial objects? If the latter, what is the name for that property? Is it the "Hubble Value"?
By analogy, we can find the mean height of people, and say we are increasing the precision of that mean height by increasing the sample size. But we can't say we are increasing the precision of the height of people. We could also use that precision of the mean to say "The mean height of men is greater than the mean height of women" but this does not preclude individual women being taller than individual men.
On the other hand, if Hubble's constant is a fundamental property of the universe, increasing the sample size makes the measure of that constant more precise. If two different experiments lead to different measures of that same constant value, then it indicates some flaw in the experiments.