This is a common problem and it is so unfair that this one person or company policy can thwart the aspirations of another. Keep documented proof of your attempts to obtain the reference letter. Collect proof of the policy if the company has one that prohibits giving reference letters. Be sure your boss understands that this is not a reference of approval, but an objective letter stating the facts surrounding the duration, duties and compensation of your work for that company.
Gather as many different documents as you can that show your duties, signing on letter, pay slips and annual income tax payments, letters from supervisors, clients or peers, etc. good luck