It’s an interesting bit of ancient word and medicine trivia but it isn’t terribly elucidating about the mechanism or course of diabetes in modern times.
Your body always has some glucose metabolism going, even if you’re in ketosis, etc there’s always “sugar metabolism” - your blood glucose doesn’t drop to 0 unless you’re dead. It’s simply not a useful abstraction to link sugar consumption to diabetes as implied by the GP.
And ultimately diabetes is defined as a condition of dysregulation of sugar in the blood.
In fact, these days most well cared for people with controlled diabetes don’t have sugar in the pee unless they’re taking a medication specifically to put it there.
Also if you want your mind blown and why you can’t diagnose based on etymology alone (at least not without a sense of humor) - lookup “diabetes insipidus”. Literally means “sweet pee that isn’t sweet”.
The historic reason is that excessive urination is common to both.