I can only point to my own experience for this thread. When I am booking a non-chain hotel, I will check both third party vendors and the actual hotel websites. If the hotel is located in another country, I have often sent them an email to clarify/confirm their website rate and ask about discounts.

For my hotel bookings, I do much better (when staying at a non-chain hotel in the US or abroad) by using a third party booking agent. The cost is always less than what the website or the hotel offers me. I did have a hotel in Florence tell me upon checking out that the next time I should call them direct and they'd beat the discounted rate I paid. That's great, but if they're willing to do that for me, they should make it easier up front. I had previously contacted them via email to verify their posted rate before I booked through the third party website. They could have offered me a discounted rate at that time.