I'd have thought it usually unnecessary to ask a landlord for references, since you have the advantage that the landlord doesn't have with a tenant of seeing how the accommodation is maintained - whether it's in good order generally, clean, reasonably freshly decorated, etc. Then if you decide you want to take the place you see how the landlord deals with your deposit (receipts and happy to take cheque or draft, or insist on a wadge of cash that they stick in their pockets!), whether they have a proper tenancy agreement, provide rent book and contact details without having to be asked, sign you up on the PRTB registration form, and so on.
Personally, I'd be surprised to be asked for a reference since all of these things should really provide the evidence, but I don't think I'd have an in principle objection so long as the prospective tenant was nice about it. Then again, my tenants' English isn't good so I'm not sure how useful a reference would be - and in any case, I'm planning to keep them for as long as they want to stay.
And I'm fairly sure some of the nightmare landlords I've had in my time would have had no difficulty in rustling up excellent and thoroughly fictitious references. I'm pretty confident that some serious problem tenants can manage the same.