No, Speed has nothing to do with accuracy & evasiveness.
1. Where did you battle it? In Battle Tower/Frontier? It might hold Brightpowder.
2. What move did you use? Not all moves has 100 accuracy......
There is a pretty good chance that it used Double Team when you weren't looking. And if they weren't, there are plenty of moves that don't hit 100% of the time, such as Rock Slide. There is no relationship between speed and evasion, as Shiny Trainer said.
Evaisivness and Speed are two different things.
Speed allows you to attack first. If you have higher speed than your opponent you will strike first.
Evaisivness allows you to dodge. Higher Evaisivness = more dodging.