This is not what double insulated means. Double insulated means that no single failure point can result in dangerous voltages (with or without equipment grounding). That could be two layers of insulation or reinforced insulation.
The ground connection can also be a critical part of an EMI reduction strategy.
The ground connection can also be a critical part of an EMI reduction strategy.
"Double-insulated" simply means anything the user would be likely to touch is made of non-conductive material. In 120V code-compliant electrical systems, the neutral conductor is also connected to ground, and thus, to the circuit breaker.