I attended a fantastic lecture on kashrus and dairy products by Rabbi Zushe Yosef Blech, shlita, who was asked an interesting question: Can you eat Oreo cookies after a fleishig meal? It was pointed out that although the kashrus symbol indicates that the product is kosher but dairy, another part of the label that must list whether there are any ingredients for which many people suffer dangerous allergies (E.g. nuts or milk), as required by the Americans with Disabilities Act, does not list dairy items at all. Rabbi Blech made the amusing comment that "Not only can you eat Oreos after a fleishig meal, it is a mitzvah to do so." He explained that the manufacturer is more concerned about getting sued by consumers who have unwittingly eaten an allergen than the rabbis certifying their product. He says that the O-U these days puts a "d" on any product where the line has been used for dairy products (and not kashered). Is this an opinion by most poskim, or is Rabbi Blech out on a limb?
Rabbi Bleich is very well-respected in the kashrus industry, and he has a tremendous amount of practical industry know-how. I'm not sure how anything he said here would be "out on a limb."
An "OU-D" can mean any of the following:
You can call the OU and ask them about a given OU-D product, "is this halachically dairy or made on dairy equipment?"
Personally I wouldn't trust the allergen label alone as proof of pareveness, but it would probably mean it's worth trying to call the OU. (Please don't bother the OU by calling to ask whether Smith's Country Vanilla Yogurt is really dairy.) If Rabbi Bleich commented about Oreos, that's because he knows exactly what goes on in their factory.