Another angle to look at is low-light. I think that would be a more realistic angle than speed. When it comes to true accuracy with group sizes, the irons are better, as you can't get quite as fine on a bullseye with a dot as you can irons. What the RDS dot does do is get faster hits on a threat than irons, so groups can easily be 5-6 inches. Show scores at a low light shoot with a RDS then Irons.
Iron sights are probably better in my opinion for patrol work if the RDS option is anything except an Aimpoint. My personal experience is that only the Aimpoints have what it takes to survive. I have an agency in my area that is fielding EoTechs and Vertex RDS's, with wandering zeros and all. They don't care about anything but $$ saved. Is that a factor in his thinking at all, or the responses that he's gotten from his sources? How old is that information he's gotten?
I guess I'm asking these questions as I'm looking at other arguements you maybe also want to head off ahead of time. Your best resource for the RDS vs Iron arguement is probably going to be one of Pat's SWAT articles otherwise as a start for sources.