Gonna have to be a physics nazi here and say not true. We are essentially dealing with two lever arms here...... the first is the radius of the wheel/tire (tyre to keep things "proper" in the context of the OP) acting on the axle. The second is the extension from the axle to the disc mounting radius, extended out to the friction plane where the calipers meet the rotor.
The interface at the caliper/rotor has to overcome the torque being generated by the larger lever arm of the wheel. A larger rotor WILL offer better counter-torque for a given amount of friction from the caliper. Please note that this WILL take LESS force from the caliper to attain when compared to a smaller rotor.
HOWEVER, as others have said, this added "power" is absorbed elsewhere in the system (increased stresses closer to the axle).

I personally feel that, if your setup is sensitive enough, the larger rotor could give you a greater range of modulation, and,yes, better ultimate stopping power.

Finally, as it has been mentioned, there might be some gremlins in the works if you can't lock up your discs, even with the 160's.