Not true. An over stable rocket will have poor dynamic response to a disturbance. People generally use "static margin of stability" as rule of thumb and do not consider dynamic stability. It's a complex subject and not simple to analyze or simulate, so most people ignore it.
Overly stable rockets are more likely to "cone" if there's a fin misalignment or thrust misalignment.
Overly stable rockets are less likely to recover from a sudden wind gust. With a high polar moment of inertia, once deflected, the rocket keeps rotating while the fins attempt to correct the angle of attack. If it can correct in time, it will be stuck at a new path off vertical.
Another dynamics problem, consider two rockets could have the same mass and the same static margin of stability, but the mass is distributed differently. The one with the mass distributed more toward the ends (heavy nose weight and heavy motor) will have a higher moment of inertia, and will respond slower to disturbances (over damped). For the rocket with evenly distributed mass, the correcting moments from the fins will quickly respond to the delection, and possibly over correct if under-damped, bringing it back to its original vertical trajectory. Also, with heavy nose weight, the CG will shift forward more quickly as the motor burns out, creating an overly stable rocket (see above).