The hazing he is referring to sounds like what is sometimes called "deglazing" the rotor surface. The theory is that as the surface of the rotor wears, and this would depend on the pad composition, it acquires a very smooth surface. The undesirably smooth surface can cause high pitched squealing on some cars. The hazing dulls the shiny surface. Also, the purpose of the blue goo, or any other of the pastes behind the pad, is to change the natural frequency of the vibration away from the one that creates the squeal. Sort of like a dampening agent. The hazing means the mechanic would remove the shiny surface, leaving a "hazy" sort of dull appearance. I used to do this with about 400 grit paper. Same reason when you put new piston rings in, you "deglaze" the cylinder walls. Provides a new surface for the new pads (or rings) to wear on.
Deglazing (making dull) the surface, and using the paste, should stop the squeal, assuming the pads are in proper position and no other foreign material is caught in the rotor/pad (like a pebble or something...have seen this too)
Hope this helps. Dave