So, it would be wrong to label any product of one's hives as being organic. But, one could say "Produced from organically managed beehives.", right?
Well, yes, but I really think it depends on how narrowly you define the term. Webster's defines organic (in this context, which is a relatively new usage) as
3
a (1) : of, relating to, or derived from living organisms <organic evolution> (2) : of, relating to, yielding, or involving the use of food produced with the use of feed or fertilizer of plant or animal origin without employment of chemically formulated fertilizers, growth stimulants, antibiotics, or pesticides <organic farming> <organic produce>
By this definition, if your management excludes the use of these things, your honey would be "organic". Some people of course would define it more narrowly, to take into account any forage though it be beyond the control of the beekeeper.
In the end, labels like this are inadequate to their purpose, which is to allow people to make "informed choices" without ever bothering to inform themselves. For example, I have many fruit producing trees, and I use no pesticides, at all, and as a result I have pests. So I have some insect and fungal damage. There is no way to avoid it. But the "certified organic" label allows for the use of many chemicals (such as copper sulphate for fungal control, the list is actually very long). The "organic" produce many people buy? I am sorry, but it would NEVER pass the strict definition that some want to adopt for the production of honey. If you don't use ANY chemicals, you will have SOME insect and fungal damage. Yet I have never seen insect damaged produce at a place like Whole Foods. Ever.
Just some thoughts. Not saying what it right or wrong, just pointing out the futility of trying to reduce a complex issue into one word.
Cheers