I say absolutely does not have a say in the matter. At best get this candidate is certified as a rescue diver and has no say in whether the OW candidate is certified or not. As for training his only roles are to assure a fun dive and all safety requirements are met.
You are right in that the DM does not have any say in the actual passing or failing of a student but any instructor that poo poos an experienced DMs concerns is a fool begging for trouble. Granted a fresh DM straight out of a zero to hero training may not be the best judge but I have DMed for several years, been diving longer than many of our instructors and have 2 or 3 times more bottom time than some of them. If the DM sees a major issue, brings it to the attention of the instructor and the instructor either ignores it or chooses to let it go, he is setting both of them as well as the shop up for trouble. I for one would never DM for that instructor again, I am simply not going to work with an instructor who just passes student on. To me, the DMs role is a lot more than just a dive nanny and a tank monkey. I often take on the difficult students for extra help, freeing up the instructor to continue the class. We will not pass them if they are not ready and the final decision is the instructors but a good DM can take a make the difference in the student passing or worse being passed on by an overtaxed instructor. We often have big classes, I am DMing for a class of 9 OWs now. The instructor and DM are a team who work together to give the students the best possible training while still having fun. If the instructors you work with consider you nothing more than a tank monkey and equipment gofer, find a better instructor.