OK, my first example was extreme to show how SILLY their argument is - of course water consumption / dilution matters! The more water, the lower the concentration.
The side panel on my Ketostix lists the range of pink to purple as ranging from 5 to 160 mg/dL (milligrams/deciliter). This is the standard for measuring most components of blood & urine.
If you increase the deciliters (amount of water), you decrease the concentration of ketones (milligrams) - in other words, the ketones remain the same but the extra water thins them out. So, add double the water in a moderate reading of 40, and it turns into a small reading of 20.
This is simple chemistry - if it matters to you, yes, I do have a degree in chemistry and a degree in mathematics.
There may be some deeper biochemical explanation for their contrary view that makes sense - I'd love to hear it - but on the face of it, the chemistry says they are wrong.
They may be assuming that one's water consumption stays more or less the same - this works on average, but not for everyday ups and downs in water, temperature, exercise, etc.
back at you!