I don't automatically believe reports like this, but by the same token, I don't automatically disbelieve reports like this. I'd add that the more often that's reported by credible people, the more likely that premonitory dreams actually happen.
Speaking of predictive dreams, here's a weird one for you. A little over 20 years ago I had a vivid dream one Saturday morning where I was standing on a dock in Haiti, beside a ship I came on, wearing a goofy safari hat, and listening to a Haitian tell me a story about how his little daughter had been taken from him by practitioners of Voodoo. I woke up, thought it was weird and half wondered if that dream could have been given me by God. Then I immediately dismissed that idea and thought it was silly because why in Heaven's name would I go on a ship? No one goes anywhere on a ship anymore. If I was going to go to Haiti I'd go on a plane, and I certainly wouldn't be wearing a stupid safari hat. Besides, I didn't really believe in that sort of thing anyway. So I dismissed the dream and quickly forgot about it.
A year or two later an opportunity was presented to me to go with a mission team to Haiti to help build an orphanage and school in a little village on top of a mountain near Port au Prince. I accepted, raised the money, and off I went...on a ministry ship. So, what happened? On the dock in Haiti immediately after arriving I met a man and had a long conversation with him about Christ, and eventually he started telling me a story about how his little daughter had been taken from him by practitioners of Voodoo. The second he told me that, memories of the dream came flooding back, and with a stunned look on my face and my friend immediately asking me what was wrong with me, I looked over my shoulder at the ship I had come on, looked again at the man who had just told me the story, and then took off my, yes, totally goofy safari hat that I can't believe I was wearing.
There are a ton of things from that trip that I won't go into, except to say that it truly transformed my life and gave me a heart for missions and the poor from that day forward. But on the topic of dreams...you tell me...was the dream a predictive dream providentially given by God or was it the weirdest coincidence in human history? Nothing like that had ever happened before or since, but it is something I've always treasured but rarely told anyone about.
Oh, and one little humorous aside about the goofy hat. When we got up to the village and everyone was very nervous (both us and the villagers), someone on our team yelled at me to throw him my goofy hat. Lo and behold it sailed through the sky like a Frisbee. So, before you know it our team and virtually the entire village were in a giant circle playing a game throwing my stupid hat across the circle to each other and trying to catch it on our heads. That hat ended up being be best ice-breaker I've ever seen. We all had so much fun it was like we had been friends forever by the time we stopped playing and got down to the business of unloading gear and getting our work started.