Is this LED slow, or am I measuring it incorrectly?
The response time is strongly dependent on the phosphor type used. 

The YAG type yellow phosphor is pretty fast (should be sub-microsecond) but they may be using a different type of phosphor in that particular LED. There's also no guarantee they will stick with that particular phosphor. 

I suggest using a blue filter and compare the response time of the blue driving LED die. If it's still very slow you may have to improve the LED drive circuit. If the speed is much faster you might want to try another type of white LED or use an RGB LED.