If a product is labeled dairy, but the allergen information says "may contain traces of milk," can I assume that it is actually only dairy equipment? If it didn't say anything, maybe they just didn't list it, which I have heard is done. But if it does list it, but says "may contain," is that reliable?
You should check with the authority who gives the Hechsher (Kashrut certification). Sometimes the OU will put OU(D) on products that are merely made on dairy equipment but are not actually dairy, but there may be a very good reason as to why they put OU(D).
Due to a change in labelling regulations, there is generally an allergen warning on products which, although not containing Dairy ingredients, are processed in close proximity to or in the same factory as, products containing Dairy ingredients. Such products may still have the halachic status of Parev, even when bearing the warning ‘contains traces of milk’. The KLBD always takes into account shared use of production equipment and cleandown procedures when determining the kosher status of a product.
Some Green & Black’s Organic chocolate is listed by the Guide as P = parev. See below
P Dark Chocolate 70%
P Dark Chocolate 85%
What has changed with your milk allergen labelling?
WHY HAS THE ALLERGEN WARNING CHANGED?
The new communication will highlight milk as an ingredient in its previously labelled ‘vegan’ dark organic chocolate bars. As both the milk chocolate and dark chocolate bars are made using the same production line there is a risk of cross contact. A recent audit revealed that traces of milk residues can still be found on manufacturing equipment despite intensive cleaning.
So it is possible to find parev products labelled as containing milk.
London Beth Din seem to take the position that products not containing Dairy ingredients, processed on the same intensively cleaned equipment as products containing Dairy ingredients can still have the halachic status of Parev.
If a product is labelled dairy, certainly according to LBD, there is real reason to think it contains important quantities of milk. As Big Joe says "check with the authority who gives the Hechsher".