Ok, I think the confusion here is stemming from the fact that no where on this thread have we actually defined "honeydew". Honeydew is the waste excretion of certain insects that feed on plant sap (think aphids, scale bugs, etc.) These insects have piercing mouthparts which they stab into a plant and then suck out its internal juices. Because these bugs eat only plant sap though, they need to eat copious amounts of it to get enough protein in their diet, way more than their tiny stomachs can hold, and they end up ingesting way more sugars than they need for their own carbohydrate intake, just to get the other nutrients they require. As a result their digestive tracts move really quickly, and a lot of the sugars survive out the back end.
Their waste is therefore attractive to other insects who are searching for sugary liquids, like bees, and also ants, some of whom even farm aphids for their honeydew. This is why honeydew honey is only questionably honey, because the source for the honey is not a plant, it's an insect.
Now, cotton. Cotton flowers, which should have been obvious to me if I was thinking about it. There are obviously seeds in cotton bolls, hence the invention of the cotton gin, and where there are seeds, there are flowers (or cones, but obviously cotton plants don't make pine cones). Cotton is self-pollinating, so it doesn't require bees, but, as you mentioned Phillip, cotton will increase its yield when cross-pollinated by insects. So cotton does produce nectar, both in its short-lived flowers and in extra-floral nectaries outside of flowers, in this case on the leaves. Which means cotton honey is honey, because it's made from plant nectar.