Gravity - the earth moves towards the free-falling bowling ball and the feathers?

so, Prof Bri Cox (he’d like me crimping his first name to Bri like that, it’s cool) goes to Nasa’s Space Power Facility near Cleveland Ohio to demonstrate how a heavy object (a bowling ball) and a light object (feathers) fall to the ground at the same time, as long as you remove the air-resistance from the free-falling equation.

Stunning experiment gives hard evidence, but is it really true that, as Einstein suggested in his Equivalence Principle, “…both the bowling ball and the feathers AREN’T MOVING…” the only way this could happen is if the Earth is (somehow) moving towards the free-falling bowling ball or feathers at all times. In fact, the Earth (whatever it really is) must be micro-to-macro expanding, moving or ‘growing’ at all times away from its core (in some as-yet-unformulated way) while we stand in space, unmoving.

But… what? Really? That’s not what they teach us at school – so what’s the point of ‘going’?