The key issue is that DREME is looking at your sequences as a whole, while FIMO looks at each match independently from all the others. Having many weak matches can provide strong evidence for the presence of a motif, but any individual weak match might be just a chance occurrence. The problem is exacerbated when you are working with very short motifs. The likelihood of observing a match given that it is an instance of the motif can never be very different from the likelihood of observing that same match given that it was generated randomly from the background model.
Consider this analogy: suppose you have a machine that makes coins for gambling. Unfortunately the machine is not very consistent, and some coins come out biased (not 50:50). As each coin comes out, you flip it once and record whether it landed heads or tail. Suppose that after the machine has generated 1000 coins, you've recorded 750 heads and 250 tails. That would be incredibly strong evidence that the machine is making biased coins. Now you pick up one of the coins and flip it again. It comes up heads. That would be very, very weak evidence that that particular coin is biased.