In Chiang Mai there are so many factors it's difficult to say why you might be given such an answer. But I can assure you, not only is it possible for tourists to get a COR in Chiang Mai, they can also get it the next day. I know, as I got my license in Chiang Mai doing exactly this when I had visa exempt.
You submit your application and ask for expedited processing. Costs 500 baht, no receipt, and you pickup the next day.
Reasons that might cause them to tell you no to either getting a COR at all, or getting the next day COR:
Too many people in line
Already committed to too many expedited certificates for the next day
Other immigration officers nearby
Supervisor/superiors nearby
It's a day that ends in y and the officer doesn't feel like it
For Chiang Mai, either wait until there are less people in line and no one is around and ask again, or come back another day and try again.