You've hit on the flaw in the rubbish that's dished out to the newly diagnosed by the diabetic advisors ie. doctors, nurses, dieticians. The "plate" they are so keen on showing shows foods with high sugars and fats separately from carbs. This confused the hell out of me until I got to grips with it.
I have never had a sweet tooth so was a little stuck when I was told to reduce things I never ate in the first place! I was told to use sweetners in my tea and coffee: a bit tricky since I've not liked any sweetening in drinks for 50 years! When I said this, I got a look that I interpreted as dibelief. It gradually dawned on me that it was assumed I was eating a diet at odds with their recommendations as I was grossly overweight.
I didn't get to be overweight until I started "healthy eating"! I now follow a low carb/ high fat diet and finally got some control on both my weight and BG.
The reason I rambled a bit here is becuse I initially thought, as I didn't eat sweet things, I was doing it right! Like you I checked sugar content and didn't worry about total carbs. My doctor's advice was "watch your diet, particularly sweet things and take the Metformin". Through books and this forum, I learned that carbs are carbs - as Ken so rightly says.
I forgot to mention they also ignore the carbs in fruit and vegetables!
Ray