No sugar refers to non processed sugar byproducts (i.e. cane, beet, corn, or any other food based extracted concentrated sugar).
Honey is technically not included (provided that it is from the wild and raw). That being said, I don't recommend smathering honey on everything. Occasional use is acceptable.
We get the natural sugars that we need by consuming real food – whole organic fruits and vegetables.
Some people have difficulty with certain fruits because of allergies, some because of pre-existing digestive disease (lack enzymatic ability to break them down).
The take away here is – sugar that is naturally found in real food is ok to eat.
Sugar that is extracted from food is better left alone.
Hope this helps clarify for you.
Have a great day!