"... is that all objects in the Universe can detect no difference between a constant acceleration and an acceleration due to gravity."

False. Gravity always creates a gradient. Whereas I don't think a force applied to an inertial mass creates a gradient.

Besides: you can accelerate toward a massive object with any acceleration value... given that the spacial distortion is not too intense.

But a human body will fail to sustain an acceleration of 6g or more for long periods...