A Record of Employment is a legal requirement set by HRDC, for employment insurance purposes. It is required if the OP was paid by the hour and had an established employee relationship with the employer, and not as a contractor, I believe.
An ROE is not a reference letter. Two completely different things.
An ROE is required by Service Canada for EI purposes. Most companies also use it as a formal record of employment (which it is).
A reference letter is completely optional (unless it was negotiated into your terms of employment or is part of a collective agreement). In the absence of that, no employer is required to give you one (or even confirm your employment over the phone for that matter). In such a case you could provide a copy of your employment letter and your ROE as proof of employment (but you better have a good answer when your potential employer wants to know why you previous employer won't give you a reference).

