Squeal is not always just between the pad and the rotor. The squeal is caused by tiny rapid vibrations throughout the assembly.
This Popular Mechanics article describes it well;
Under the right conditions, the disc, the pads and the caliper they're
mounted in can start to vibrate—in exactly the same way a violin's
string vibrates when stroked by the horsehairs on the bow.
Ways to avoid this are,
- Use coated shims or the anti-squeal compound between the caliper and
- Lube the caliper slides to ensure the caliper is free to float (corrosion can buildup causing them to bind).
- Have the rotors machined or replaced to ensure they are true.