Patently false.
Dive recovery altitude loss is a function of radial "G" available & airspeed only - physical dimensions or engine size of the aircraft has nothing to do with the physics and aerodynamics of it. See:
http://apstraining.com/blog/2009/10/...from-the-dive/ , specifically figure 2. Note the absence of any size factors in the calculation for turn radius.
Slow the airplanes down and the airspace can be smaller. Enhance aerodynamics to give more lift, and therefore more "G" (along with strengthened airframe), then the airpace can be smaller. Of course one could always just design competitive maneuvers that require less airspace too.