Your incorrect assertion proves my point. You claim the single "right" way to measure height is without shoes using a stadiometer. However, this is not always an accurate or reproducible approach because it's difficult to ensure consistent posture when using devices like these. Different operators of the stadiometer get different results measuring the same person because they will encourage the person being measured to stand differently.
You can read a paper about the challenges in measuring human height accurately and precisely if you like:
http://adc.bmj.com/content/65/12/1340.full.pdf
Furthermore, many doctors record the heights of patients in shoes. You may think it's "wrong" of them to do that, but they disagree. Additionally, you're ignoring the reality that the NBA records the heights of players
wearing shoes. It's not "wrong" to do that either. A person's height in shoes is the height they're interested in.
The fact is - measuring the human body accurately and precisely is not simple to do. It's not like measuring a block of wood.