The person obviously misspoke about the meaning of OU-D.
The label may have been placed there for a number of reasons: that there are dairy ingredients, that they are manufactured on equipment that is used to process dairy, that any of the component ingredients have been derived from dairy products or have been processed on dairy equipment, or simpy that the company wants to  leave itself some flexibility as to how these cookies are manufactured and doesn't see a significant market risk in labeling them as dairy.
 In these cases, it's a calculated but relatively small risk. It's up to you if you want to try such foods, but wise to do so in controlled circumstances (i.e., not on an airplane at 30,000 feet). And if such foods appear to be safe, it's an ongoing risk that the manufacturer may opt to "earn" the Dairy label.
We've found mixed results with foods labeled OU-D but without dairy ingredients. They have not yet triggered anaphylaxis in our son, but occasionally have made him more itchy than normal. We try to limit his intake, but it's hard with a food that's that appealing. If it were my child (and he were much younger), I'd secretively buy a package, hide it, and give him a small piece, with resuce meds at hand. After maybe 1/2 hour, some more, and them some more, watching for a reaction. Then I'd back off for a day or two and watch for any symptoms. Without any, I'd try a cookie at a time and watch. I'd also be watching at each new package or lot. Moderation is key, although a challenge for yummy treats.
G'Luck,
Mark