According to the certifying agency of Nabisco Oreo cookies, which are marked OU-D:
The equipment is not necessarily cleaned before the production of these cookies, and there may be a small amount of dairy residue present. Nonetheless, the dairy component would be minimal, and from a Halachic perspective, the dairy residue is nullified (botel bishishim) and of no consequence. The bottom line of all this is that these cookies may be consumed after meat and poultry, but not simultaneously.
IMSMC, according to the Maharshal, being stringent by not relying on the halachik principle of nullification (bittul) is considered heretical/quasi-heretical (as unjustified rejection of a traditional halachik principle; as opposed to the traditional principle of ein mevatlin issur l'chatchila - not intentionally nullifying forbidden food). Nonetheless, this does not appear to reflect normative practice.
However, in the case of "dairy" equipment, there appears to be the added issue that it is not clear that there was even bittul to begin with (i.e. based on the language cited above, it seems there is at least an additional uncertainty whether any given cookie has even a trace amount of dairy).
Accordingly, which halachic authorities (rishonim and/or achronim) does the OU rely on in crafting its ruling that even an alleged uncertainty (safek) of a possible trace amount of heter dairy should nonetheless prevent eating the overall product together with meat (assuming, of course, that Oreos are considered nosein taam lishvach [tasty] in a cholent)?