I don't think you can get a proper repair done without draining. Is this one flake the only area in the pool that has chipped? I'd be concerned, based on the location, that it's a stress area that might continue to crack.
Edit: How big is that area in your second picture? Is it the size of the flake in your hand or is it bigger? Hard to see but it looks like it's delaminating more at the bottom(?)
They ask questions about water chemistry, pool chlorine, etc, so they can blame any issues on you!!! (Pool Building 101)