I just got back from the Dolphin and they had strong, real coffee in Tubby's, the cafeteria downstairs at the Dolphin. I bought the reusable mug and refilled, often. Delicious! Got me going on those chilly post-Christmas mornings.
I also saw that on one of the urns, there was a little sign that said "We use Starbucks coffee" or something to that effect.
FWIW, Swan & Dolphin policies are a little different, as the hotels are owned by Starwood (I believe they're Westin/Sheraton). For example, refillable mug holders could only be refilled with coffee or soda - no tea, hot chocolate or soda slushies, as you're allowed in some of the other Disney properties. But as I said, the coffee made it worthwhile....