It isn't squeaking from the in-out motion. It is squeaking because it is fluttering between the rotor surface and the caliper piston/housing. Yes, the pads are not clamped solid against the rotor. They are just tight enough to give the braking friction desired. The combination of friction force on the pad face and the resisting force of the steel pad base are not exactly in a straight line. There is an offset of about the thickness of the pad. This produces a left-right torque on the pad, which changes the pad pressure and point of application slightly... which changes that torque... which changes the pad pressure again... on and on. At some point, all these physical forces and slight pad movements hit a resonant frequency. The pads, caliper, and rotor are all rather robust and stiff pieces, so the resonant frequency is bound to be high.
The sound itself may well be from the rotor vibrating, it is a big "sound board", but I am pretty sure the mechanical forces that cause the rotor to vibrate are as I attempted to describe above