That statement is true. I think you are getting confused between "extruder" and "nozzle".
The extruder is the mechanism that pushes the filament to the nozzle. Most extruders pinch the filament to gain traction to allow it to push. What Lulzbot is telling you is that the extruder is designed to grab onto 2.85mm (3mm) filament but CAN grip onto 1.75mm but not as well. This has nothing to do with nozzle size.
Now, speaking of nozzle size, smaller nozzles DO work better with smaller diameter filament. What is better is resolution which equates to better control of how much plastic is being extruded at any given point in the printing process. During one step of the extruder stepper, more plastic will be extruded using 3mm filament then with 1.75mm. Therefor, extruder resolution will be much higher using the 1.75mm over the 3mm. When using larger nozzles, this does not have as much of an effect as much more plastic is being requested at a time causing the need for more steps to be used negating the need for the higher resolution.